Case3 Galferie lafayette
Raiyan Puntel and Mahmoud Alkheja
2023-04-11
rm(list = ls()) #Clean the entire environment
cat("\014") # clean consoleLoading libraries and Reading the data set:
## set library
library(lavaan)
library(semPlot) #for visualization
library(knitr)
library(dplyr)
library(lavaanPlot)
library(lm.beta)
library(rcompanion) #Histogram and Normal Curve
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr) #VIF and Tolerance Values
library(pastecs)
library(REdaS) #Bartelett's Test
library(psych) # principal axis factoring
library(naniar) # for missing values analysis
library(RColorBrewer)
library(ggcorrplot)
library(psy)setwd("/Users/mahmoudalkheja/Desktop/Advanced Data Driven Decision Making/Case Study III-20230420")
myData <- read.csv("Case Study III_Structural Equation Modeling.csv")
explanation <- read.csv("Variables and Labels_Galeries Lafayette.csv")myData =data.frame(sapply(myData,function(x) ifelse((x==999),NA,as.numeric(x))))Change 999 in the Data-set to NA’s:
Exploratory factor analyses
Conducting the confirmatory factor analyses run an exploratory factor analyses in R to get an initial idea by which dimensions customers perceive Gallerias Lafayette. In the file all 22 image items are proposed to measure different constructs or perceptual dimensions
Explore the data
head(myData)## Im1 Im2 Im3 Im4 Im5 Im6 Im7 Im8 Im9 Im10 Im11 Im12 Im13 Im14 Im15 Im16 Im17
## 1 7 7 4 4 4 7 NA NA 6 7 7 6 4 7 5 5 4
## 2 4 4 NA 4 3 5 3 5 4 5 4 5 5 5 4 4 4
## 3 5 5 7 7 7 4 NA 6 6 7 7 7 7 7 6 6 6
## 4 5 5 5 5 5 4 4 4 4 4 6 6 6 5 6 5 4
## 5 4 4 4 3 5 4 4 4 3 6 5 4 4 6 4 3 3
## 6 4 4 5 5 NA 4 2 5 3 3 5 3 3 NA 3 3 5
## Im18 Im19 Im20 Im21 Im22 C_CR1 C_CR2 C_CR3 C_CR4 C_REP1 C_REP2 C_REP3 COM_A1
## 1 4 5 4 5 4 6 6 6 6 5 NA 5 5
## 2 3 2 2 6 2 1 NA NA NA 3 4 4 NA
## 3 5 6 7 7 6 NA 1 1 2 5 5 5 4
## 4 4 5 4 3 2 2 4 5 3 4 5 5 5
## 5 3 3 3 3 3 2 7 2 1 4 5 5 4
## 6 5 3 4 5 5 5 7 5 2 5 5 5 NA
## COM_A2 COM_A3 COM_A4 SAT_1 SAT_2 SAT_3 SAT_P1 SAT_P2 SAT_P3 SAT_P4 SAT_P5
## 1 6 6 4 6 6 6 6 7 7 6 6
## 2 1 1 1 4 4 4 NA NA 5 5 5
## 3 NA 6 3 7 7 7 7 7 7 7 7
## 4 4 2 3 5 4 NA 4 4 4 3 3
## 5 4 3 3 NA 4 4 4 4 4 3 3
## 6 2 NA 2 4 5 NA 2 3 3 4 3
## SAT_P6 TRU_1 TRU_2 TRU_3
## 1 5 7 7 7
## 2 NA 4 NA NA
## 3 7 NA 6 6
## 4 3 2 5 4
## 5 3 4 4 4
## 6 4 5 4 6summary(myData)## Im1 Im2 Im3 Im4 Im5
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.00
## Median :5.000 Median :5.000 Median :5.000 Median :5.000 Median :5.00
## Mean :4.792 Mean :4.854 Mean :4.985 Mean :5.002 Mean :5.04
## 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.00
## Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.00
## NA's :14 NA's :18 NA's :20 NA's :10 NA's :29
## Im6 Im7 Im8 Im9 Im10
## Min. :1.000 Min. :2.00 Min. :1.000 Min. :1.000 Min. :2.000
## 1st Qu.:5.000 1st Qu.:5.00 1st Qu.:6.000 1st Qu.:4.000 1st Qu.:6.000
## Median :6.000 Median :6.00 Median :6.000 Median :5.000 Median :6.000
## Mean :5.824 Mean :5.75 Mean :5.996 Mean :5.076 Mean :6.102
## 3rd Qu.:7.000 3rd Qu.:7.00 3rd Qu.:7.000 3rd Qu.:6.000 3rd Qu.:7.000
## Max. :7.000 Max. :7.00 Max. :7.000 Max. :7.000 Max. :7.000
## NA's :9 NA's :26 NA's :6 NA's :16 NA's :6
## Im11 Im12 Im13 Im14
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:5.000 1st Qu.:5.000 1st Qu.:5.000 1st Qu.:6.000
## Median :6.000 Median :6.000 Median :6.000 Median :6.000
## Mean :5.654 Mean :5.665 Mean :5.444 Mean :6.144
## 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:7.000
## Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
## NA's :12 NA's :21 NA's :15 NA's :24
## Im15 Im16 Im17 Im18 Im19
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:4.00 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.000
## Median :5.000 Median :5.00 Median :5.000 Median :5.000 Median :5.000
## Mean :5.098 Mean :5.13 Mean :5.018 Mean :4.571 Mean :5.148
## 3rd Qu.:6.000 3rd Qu.:6.00 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.000
## Max. :7.000 Max. :7.00 Max. :7.000 Max. :7.000 Max. :7.000
## NA's :12 NA's :24 NA's :12 NA's :28 NA's :12
## Im20 Im21 Im22 C_CR1
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:3.000 1st Qu.:1.000
## Median :5.000 Median :5.000 Median :4.000 Median :2.000
## Mean :4.669 Mean :5.135 Mean :4.289 Mean :2.674
## 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:4.000
## Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
## NA's :9 NA's :5 NA's :17 NA's :20
## C_CR2 C_CR3 C_CR4 C_REP1 C_REP2
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:3.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:4.000 1st Qu.:4.00
## Median :5.000 Median :3.000 Median :2.000 Median :4.000 Median :5.00
## Mean :4.616 Mean :3.271 Mean :2.796 Mean :4.281 Mean :4.51
## 3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:5.000 3rd Qu.:5.00
## Max. :7.000 Max. :7.000 Max. :7.000 Max. :5.000 Max. :5.00
## NA's :30 NA's :6 NA's :10 NA's :5 NA's :16
## C_REP3 COM_A1 COM_A2 COM_A3 COM_A4
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:3.00 1st Qu.:2.000 1st Qu.:2.000
## Median :5.000 Median :4.000 Median :4.00 Median :3.000 Median :3.000
## Mean :4.682 Mean :4.302 Mean :3.88 Mean :3.536 Mean :3.456
## 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.00 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :5.000 Max. :7.000 Max. :7.00 Max. :7.000 Max. :7.000
## NA's :18 NA's :14 NA's :11 NA's :18 NA's :9
## SAT_1 SAT_2 SAT_3 SAT_P1 SAT_P2
## Min. :2.000 Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:5.000 1st Qu.:5.000 1st Qu.:5.00 1st Qu.:5.000 1st Qu.:5.000
## Median :6.000 Median :6.000 Median :6.00 Median :6.000 Median :6.000
## Mean :5.349 Mean :5.481 Mean :5.45 Mean :5.424 Mean :5.486
## 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.00 3rd Qu.:6.000 3rd Qu.:6.000
## Max. :7.000 Max. :7.000 Max. :7.00 Max. :7.000 Max. :7.000
## NA's :5 NA's :10 NA's :40 NA's :8 NA's :16
## SAT_P3 SAT_P4 SAT_P5 SAT_P6 TRU_1
## Min. :1.000 Min. :2.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:5.000 1st Qu.:5.000 1st Qu.:4.00 1st Qu.:5.000 1st Qu.:3.000
## Median :6.000 Median :6.000 Median :6.00 Median :6.000 Median :5.000
## Mean :5.406 Mean :5.535 Mean :5.29 Mean :5.635 Mean :4.368
## 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.00 3rd Qu.:7.000 3rd Qu.:5.000
## Max. :7.000 Max. :7.000 Max. :7.00 Max. :7.000 Max. :7.000
## NA's :6 NA's :13 NA's :8 NA's :13 NA's :28
## TRU_2 TRU_3
## Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:5.000
## Median :5.000 Median :6.000
## Mean :5.121 Mean :5.461
## 3rd Qu.:6.000 3rd Qu.:6.000
## Max. :7.000 Max. :7.000
## NA's :33 NA's :28dim(myData)## [1] 553 45Our dataset consists of 553 observations and 45 features, but it exhibits missing values in certain portions. Additionally, all questions (Image 1 to 22) in the dataset have been scaled on a 7-point scale.
gg_miss_var(myData)
For exploratory factor analysis: we only consider variables image1 to image22, and we will use listwise deletion to handle missing data before starting.
image <- myData[,c(1:22)]
miss_var_summary(image)## # A tibble: 22 × 3
## variable n_miss pct_miss
## <chr> <int> <dbl>
## 1 Im5 29 5.24
## 2 Im18 28 5.06
## 3 Im7 26 4.70
## 4 Im14 24 4.34
## 5 Im16 24 4.34
## 6 Im12 21 3.80
## 7 Im3 20 3.62
## 8 Im2 18 3.25
## 9 Im22 17 3.07
## 10 Im9 16 2.89
## # ℹ 12 more rowsimage <- na.omit(image)
dim(image)## [1] 385 22385 observation after removing the missing values.
Normality assumption
# histograms
par(mfrow = c(3, 3))
for (i in colnames(image)) {
plotNormalHistogram(image[,i], main = paste("Frequency Distribution of", i))
}
lillie.test(image$Im1) # Kolmogorov-Smirnov-Test for normality ##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: image$Im1
## D = 0.17221, p-value < 2.2e-16lillie.test(image$Im22) # Kolmogorov-Smirnov-Test for normality ##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: image$Im22
## D = 0.15889, p-value < 2.2e-16Upon examining the histograms of the data, it appears that the normality assumption is not met. Specifically, the Kolmogorov-Smirnov test for normality on samples (Im1, Im22) yielded a small p-value, indicating that the null hypothesis that the sample comes from a normal distribution can be rejected.
Correlation matrix:
Matrix = cor(image, use="complete.obs") #We create a matrix.
ggcorrplot(round(as.matrix(Matrix), 2),
method = "square",
type = "lower",
show.diag = FALSE,
lab = TRUE, lab_col = "black", hc.order = T, lab_size = 2)
Given that most of the correlation coefficients among the variables exceed 0.3, it appears that there is a significant degree of correlation between the variables. As a result, factor analysis can be an appropriate method to extract underlying factors from these correlated variables.
Check adequacy of correlation matrix.
KMOTEST=KMOS(image)
KMOTEST##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = image)
##
## Measures of Sampling Adequacy (MSA):
## Im1 Im2 Im3 Im4 Im5 Im6 Im7 Im8
## 0.8244624 0.8224640 0.8640362 0.8542604 0.9546668 0.8224827 0.8448231 0.9300079
## Im9 Im10 Im11 Im12 Im13 Im14 Im15 Im16
## 0.9380091 0.8285789 0.9113882 0.8789413 0.8722220 0.8267452 0.9647563 0.9092200
## Im17 Im18 Im19 Im20 Im21 Im22
## 0.8644991 0.8550678 0.9400714 0.8266391 0.9149654 0.8793157
##
## KMO-Criterion: 0.8770975sort(KMOTEST$MSA)## Im2 Im6 Im1 Im20 Im14 Im10 Im7 Im4
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604
## Im18 Im3 Im17 Im13 Im12 Im22 Im16 Im11
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882
## Im21 Im8 Im9 Im19 Im5 Im15
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563KMO ( Kaiser-Meyer-Olkin ) test gives us a KMO - criterion of 0.88 which is good we need more than 0.6 for a good factor analysis. We see no gap between the variables they are all very close in KMO.
bart_spher(image)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = image)
##
## X2 = 6451.238
## df = 231
## p-value < 2.22e-16In the Bartlett’s Test of Sphericity the small p_value indicate strong evidence against the null hypothesis that CM equals to identity matrix in other word indicating that the variables in the data set are significantly correlated
Principal axes factoring
# Run factor analysis with no rotation
# ?fa # details on the function
fa_0 <- fa(image,
nfactors = ncol(image),
rotate = "none")
# Look at communalities
sort(fa_0$communalities)## Im11 Im9 Im5 Im21 Im19 Im15 Im16 Im8
## 0.6017430 0.6131069 0.6413666 0.7117001 0.7290241 0.7485245 0.7604446 0.7936975
## Im12 Im18 Im13 Im20 Im22 Im6 Im7 Im10
## 0.8132541 0.8294448 0.8417272 0.8564198 0.8745729 0.8773807 0.8937851 0.9167615
## Im2 Im3 Im17 Im4 Im14 Im1
## 0.9264859 0.9307854 0.9352630 0.9664673 0.9711077 0.9761381total_var_explained_paf <- data.frame(
Factor_n = as.factor(1:length(fa_0$e.values)),
Eigenvalue = fa_0$e.values,
Variance = fa_0$e.values/(ncol(image))*100,
Cum_var = cumsum(fa_0$e.values/ncol(image))
)
total_var_explained_paf## Factor_n Eigenvalue Variance Cum_var
## 1 1 8.97758636 40.8072107 0.4080721
## 2 2 2.46726381 11.2148355 0.5202205
## 3 3 1.56195916 7.0998144 0.5912186
## 4 4 1.45683885 6.6219948 0.6574386
## 5 5 1.24785174 5.6720533 0.7141591
## 6 6 1.14733750 5.2151705 0.7663108
## 7 7 0.81009930 3.6822696 0.8031335
## 8 8 0.71161301 3.2346046 0.8354795
## 9 9 0.56785521 2.5811600 0.8612911
## 10 10 0.45684420 2.0765645 0.8820568
## 11 11 0.36139965 1.6427257 0.8984840
## 12 12 0.33234747 1.5106703 0.9135907
## 13 13 0.29499718 1.3408963 0.9269997
## 14 14 0.28351700 1.2887137 0.9398868
## 15 15 0.24936387 1.1334721 0.9512216
## 16 16 0.22811058 1.0368663 0.9615902
## 17 17 0.20225224 0.9193284 0.9707835
## 18 18 0.18624143 0.8465520 0.9792490
## 19 19 0.15737216 0.7153280 0.9864023
## 20 20 0.11623773 0.5283533 0.9916858
## 21 21 0.10167221 0.4621464 0.9963073
## 22 22 0.08123935 0.3692698 1.0000000The first factor explains 40.80% of the total variance, indicating a relatively strong ability to capture the underlying structure of the data. Additionally, the first six factors have Eigenvalues greater than 1, collectively accounting for 76.64% of the total variance. However, the seventh and the eighth factors have an Eigenvalue less than 1. BY adding them the explained total variance will be 83.54%.
# Scree plot
ggplot(total_var_explained_paf, aes(x = Factor_n, y = Eigenvalue, group = 1)) +
geom_point() + geom_line() +
xlab("Number of factors") +
ylab("Initial eigenvalue") +
labs( title = "Scree Plot") +
geom_hline(yintercept= 1, linetype="dashed", color = "red")
According to the Kaiser criterion, we should extract factors with eigenvalues larger than 1, which would suggest retaining six factors. However, it is worth noting that the eigenvalue for the 7th factor is close to 1.
Factor rotation and factor interpretation.
fa_paf_6f <- fa(
image,
fm = "pa", # principal axis factoring
rotate = "varimax", # varimax rotation
nfactors = 6 # 6 factors
)communalities_6f <- data.frame(sort(fa_paf_6f$communality))
communalities_6f## sort.fa_paf_6f.communality.
## Im11 0.4483653
## Im9 0.4631735
## Im16 0.4655592
## Im19 0.5230760
## Im5 0.5464495
## Im18 0.5766027
## Im15 0.6320150
## Im21 0.6485197
## Im13 0.6995376
## Im17 0.7003475
## Im6 0.7061967
## Im12 0.7291158
## Im8 0.7427949
## Im14 0.7587075
## Im2 0.7621640
## Im10 0.7762828
## Im7 0.7792579
## Im20 0.7839807
## Im22 0.7907061
## Im1 0.8373896
## Im3 0.8552267
## Im4 0.9171190print(fa_paf_6f$loadings, cutoff=0.3, sort = TRUE)##
## Loadings:
## PA2 PA5 PA1 PA4 PA3 PA6
## Im6 0.622 0.544
## Im7 0.734 0.457
## Im8 0.817
## Im10 0.799
## Im14 0.791
## Im1 0.855
## Im2 0.826
## Im15 0.598
## Im3 0.832
## Im4 0.874
## Im5 0.640
## Im11 0.591
## Im12 0.792
## Im13 0.731
## Im20 0.841
## Im21 0.734
## Im22 0.788
## Im17 0.349 0.308 0.385 0.547
## Im18 0.347 0.513
## Im9 0.363 0.319 0.424
## Im16 0.485 0.373
## Im19 0.464 0.403
##
## PA2 PA5 PA1 PA4 PA3 PA6
## SS loadings 3.348 2.847 2.761 2.382 2.318 1.487
## Proportion Var 0.152 0.129 0.125 0.108 0.105 0.068
## Cumulative Var 0.152 0.282 0.407 0.515 0.621 0.688Based on the loadings of the variables and their relationship to the factors, it appears that the 6-factor model does not fit the data well. Many variables seem to have loadings on multiple factors such as lm 17 and lm9, which can indicate a lack of discriminant validity. Therefore, it may be necessary to explore other solutions.
One possible solution is to consider a 7-factor model, as suggested by the Kaiser criterion. This would involve extracting an additional factor and re-analyzing the data to assess the fit of the model.
fa_paf_7f <- fa(
image,
fm = "pa", # principal axis factoring
rotate = "varimax", # varimax rotation
nfactors = 7 # 7 factors
)communalities_7f <- data.frame(sort(fa_paf_7f$communality),
sort(fa_paf_6f$communality))
communalities_7f## sort.fa_paf_7f.communality. sort.fa_paf_6f.communality.
## Im11 0.4449125 0.4483653
## Im9 0.4559063 0.4631735
## Im16 0.4734149 0.4655592
## Im19 0.5297997 0.5230760
## Im5 0.5437903 0.5464495
## Im15 0.6317519 0.5766027
## Im21 0.6494567 0.6320150
## Im13 0.6999080 0.6485197
## Im8 0.7217525 0.6995376
## Im18 0.7256024 0.7003475
## Im6 0.7644746 0.7061967
## Im2 0.7824128 0.7291158
## Im22 0.7879817 0.7427949
## Im20 0.7883146 0.7587075
## Im14 0.8099945 0.7621640
## Im12 0.8302990 0.7762828
## Im7 0.8473835 0.7792579
## Im1 0.8575489 0.7839807
## Im3 0.8613613 0.7907061
## Im10 0.8910746 0.8373896
## Im17 0.9223516 0.8552267
## Im4 0.9700881 0.9171190print(fa_paf_7f$loadings, cutoff=0.3, sort=TRUE)##
## Loadings:
## PA5 PA1 PA3 PA2 PA4 PA7 PA6
## Im1 0.860
## Im2 0.833
## Im15 0.586
## Im3 0.828
## Im4 0.903
## Im5 0.628
## Im20 0.846
## Im21 0.734
## Im22 0.784
## Im8 0.630 0.509
## Im10 0.874
## Im14 0.810
## Im11 0.579
## Im12 0.853
## Im13 0.716
## Im6 0.826
## Im7 0.322 0.836
## Im17 0.822
## Im18 0.731
## Im9 0.332 0.454
## Im16 0.458 0.339
## Im19 0.435 0.368
##
## PA5 PA1 PA3 PA2 PA4 PA7 PA6
## SS loadings 2.689 2.627 2.306 2.301 2.211 2.174 1.682
## Proportion Var 0.122 0.119 0.105 0.105 0.101 0.099 0.076
## Cumulative Var 0.122 0.242 0.346 0.451 0.552 0.650 0.727After implementing a 7-factor model, it appears that the results have improved. However, there are still some variables that have loadings on multiple factors such as lm 8,lm 16 and lm 19, which suggests a lack of discriminant validity. Additionally, there are some variables with low loading values such as lm15 and lm 11, indicating that they may not be contributing much to the underlying factors. Let’s try to interpret the results :
What do GLB represent from your point of view? Large Assortment
What do GLB represent from your point of view? Assortment Variety
What do GLB represent from your point of view? Artistic Decoration of Sales Area
What do GLB represent from your point of view? Creative Decoration of Sales Area
What do GLB represent from your point of view? Appealing Arrangement of Shop Windows
What do GLB represent from your point of view? France
What do GLB represent from your point of view? French Savoir-vivre
What do GLB represent from your point of view? Expertise in French Traditional Cuisine
What do GLB represent from your point of view? French Fashion
What do GLB represent from your point of view? Gourmet Food
What do GLB represent from your point of view? High-quality Cosmetics
What do GLB represent from your point of view? Luxury brands
What do GLB represent from your point of view? Up to date Designer Brands
What do GLB represent from your point of view? Gourmet specialties
What do GLB represent from your point of view? Professional Selection of Brands
What do GLB represent from your point of view? Professional Appearance Towards Customers
What do GLB represent from your point of view? Are Trendy
What do GLB represent from your point of view? Are Hip
What do GLB represent from your point of view? Professional Organization
What do GLB represent from your point of view? Relaxing Shopping
What do GLB represent from your point of view? A Great Place to Stroll
What do GLB represent from your point of view? Intimate Shop Atmosphere
Factors interpretation
PA5 -> 1,2,15,16,19 –> Variety ( Im15 has a low loading seem to be not relevant and more about professional,lm16 and lm19 have loadings on PA1 as well and it is about professiona)
PA1 –> 3,4,5,16,19 –> Decoration
PA3 –> 20,21,22 –> Atmosphere or Ambiance
PA2 –> 8,10,14 –> Food or Cuisine ( Im 8 has as well a loading on factor 7 )
PA4 –> 9,11,12,13 –> Brand (Im11 has a low loading )
PA7 –>6-7-8-9 –>Related to France (lm8 and lm9 have loadings on other factors)
PA6 –> 17 , 18 –> Fashion or mode.
fa_paf_8f <- fa(
image,
fm = "pa", # principal axis factoring
rotate = "varimax", # varimax rotation
nfactors = 8 # 8 factors
)communalities_8f <- data.frame(sort(fa_paf_8f$communality),
sort(fa_paf_7f$communality),
sort(fa_paf_6f$communality))
communalities_8f## sort.fa_paf_8f.communality. sort.fa_paf_7f.communality.
## Im11 0.4457585 0.4449125
## Im9 0.4555544 0.4559063
## Im5 0.5764184 0.4734149
## Im19 0.6245858 0.5297997
## Im15 0.6464069 0.5437903
## Im21 0.6464327 0.6317519
## Im13 0.6993955 0.6494567
## Im8 0.7249609 0.6999080
## Im18 0.7554077 0.7217525
## Im6 0.7604978 0.7256024
## Im16 0.7848879 0.7644746
## Im22 0.7849973 0.7824128
## Im20 0.8085432 0.7879817
## Im2 0.8155382 0.7883146
## Im12 0.8373341 0.8099945
## Im7 0.8474823 0.8302990
## Im14 0.8534420 0.8473835
## Im3 0.8559235 0.8575489
## Im10 0.8980931 0.8613613
## Im17 0.9053933 0.8910746
## Im1 0.9324261 0.9223516
## Im4 0.9691025 0.9700881
## sort.fa_paf_6f.communality.
## Im11 0.4483653
## Im9 0.4631735
## Im5 0.4655592
## Im19 0.5230760
## Im15 0.5464495
## Im21 0.5766027
## Im13 0.6320150
## Im8 0.6485197
## Im18 0.6995376
## Im6 0.7003475
## Im16 0.7061967
## Im22 0.7291158
## Im20 0.7427949
## Im2 0.7587075
## Im12 0.7621640
## Im7 0.7762828
## Im14 0.7792579
## Im3 0.7839807
## Im10 0.7907061
## Im17 0.8373896
## Im1 0.8552267
## Im4 0.9171190print(fa_paf_8f$loadings, cutoff=0.3, sort=TRUE)##
## Loadings:
## PA1 PA3 PA4 PA7 PA2 PA5 PA6 PA8
## Im3 0.812
## Im4 0.892
## Im5 0.648
## Im20 0.858
## Im21 0.733
## Im22 0.782
## Im11 0.579
## Im12 0.860
## Im13 0.720
## Im6 0.828
## Im7 0.843 0.302
## Im8 0.538 0.587
## Im10 0.867
## Im14 0.832
## Im1 0.876
## Im2 0.823
## Im17 0.808
## Im18 0.755
## Im16 0.758
## Im19 0.302 0.548
## Im9 0.334 0.460
## Im15 0.466 0.392
##
## PA1 PA3 PA4 PA7 PA2 PA5 PA6 PA8
## SS loadings 2.477 2.345 2.262 2.260 2.162 2.107 1.661 1.355
## Proportion Var 0.113 0.107 0.103 0.103 0.098 0.096 0.075 0.062
## Cumulative Var 0.113 0.219 0.322 0.425 0.523 0.619 0.694 0.756Based on our initial analysis, an 8-factor solution appears to be a good fit for our data. However, to further refine our results, we will re-do the analysis after removing variables 8,9 and 15 since they have low loading on two factors.
fa_paf_8f_n <- fa(
image[,-c(8,9,15)],
fm = "pa", # principal axis factoring
rotate = "varimax", # varimax rotation
nfactors = 8 # 8 factors
)## maximum iteration exceeded## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefullycommunalities_8f_n <- data.frame(sort(fa_paf_8f_n$communality))
communalities_8f_n## sort.fa_paf_8f_n.communality.
## Im11 0.4329273
## Im5 0.5793745
## Im21 0.6382830
## Im16 0.6436939
## Im13 0.6968226
## Im18 0.7078105
## Im19 0.7275401
## Im7 0.7395077
## Im14 0.7737207
## Im2 0.7782390
## Im22 0.7854382
## Im20 0.8153635
## Im3 0.8550184
## Im12 0.8670082
## Im6 0.9011484
## Im17 0.9643328
## Im4 0.9682718
## Im1 0.9792472
## Im10 1.0096155print(fa_paf_8f_n$loadings, cutoff=0.3, sort=TRUE)##
## Loadings:
## PA1 PA3 PA4 PA5 PA2 PA7 PA6 PA8
## Im3 0.813
## Im4 0.892
## Im5 0.653
## Im20 0.864
## Im21 0.728
## Im22 0.789
## Im11 0.566
## Im12 0.881
## Im13 0.720
## Im1 0.896
## Im2 0.788
## Im10 0.936
## Im14 0.762
## Im6 0.911
## Im7 0.318 0.761
## Im17 0.855
## Im18 0.723
## Im16 0.651
## Im19 0.664
##
## PA1 PA3 PA4 PA5 PA2 PA7 PA6 PA8
## SS loadings 2.427 2.296 2.083 1.791 1.778 1.682 1.613 1.193
## Proportion Var 0.128 0.121 0.110 0.094 0.094 0.089 0.085 0.063
## Cumulative Var 0.128 0.249 0.358 0.453 0.546 0.635 0.720 0.782fa.diagram(fa_paf_8f_n)
Factors interpretation
PA1 –> 3,4,5 –> Decoration
PA3 –> 20,21,22 –> Atmosphere or Ambiance
PA4 –> 11,12,13 –> Brand
PA5 -> 1,2 –> Variety
PA2 –> 10,14 –> Food or Cuisine
PA7 –> 6-7 –> Related to France
PA6 -> 17-18 ->Fashion or Mode
PA8 -> 16-19 ->Professionalism
PCA
# run factor analysis
fa_pca <- principal(
image,
rotate="none",
scores=TRUE)
# data frame with eigenvalues
pca <- data.frame(
Factor_n = as.factor(1:length(fa_pca$values)),
Eigenvalue_PCA = fa_pca$values,
Eigenvalue_PAF = fa_0 $e.values
)
pca## Factor_n Eigenvalue_PCA Eigenvalue_PAF
## 1 1 8.97758636 8.97758636
## 2 2 2.46726381 2.46726381
## 3 3 1.56195916 1.56195916
## 4 4 1.45683885 1.45683885
## 5 5 1.24785174 1.24785174
## 6 6 1.14733750 1.14733750
## 7 7 0.81009930 0.81009930
## 8 8 0.71161301 0.71161301
## 9 9 0.56785521 0.56785521
## 10 10 0.45684420 0.45684420
## 11 11 0.36139965 0.36139965
## 12 12 0.33234747 0.33234747
## 13 13 0.29499718 0.29499718
## 14 14 0.28351700 0.28351700
## 15 15 0.24936387 0.24936387
## 16 16 0.22811058 0.22811058
## 17 17 0.20225224 0.20225224
## 18 18 0.18624143 0.18624143
## 19 19 0.15737216 0.15737216
## 20 20 0.11623773 0.11623773
## 21 21 0.10167221 0.10167221
## 22 22 0.08123935 0.08123935The eigenvalues obtained from performing PAF and PCA factor analyses exhibit a high degree of similarity and often yield identical results. This is a common occurrence in these types of analyses.
fa_pca_7f <- principal(
nfactors = 7,
image,
rotate="varimax",
scores=TRUE # If TRUE, find component scores
)
pca_communalities_7f <- data.frame(fa_pca_7f$communality,
fa_paf_7f$communality)
pca_communalities_7f## fa_pca_7f.communality fa_paf_7f.communality
## Im1 0.8940147 0.8575489
## Im2 0.8866154 0.7824128
## Im3 0.8813179 0.8613613
## Im4 0.9113509 0.9700881
## Im5 0.7762818 0.5437903
## Im6 0.8218616 0.7644746
## Im7 0.8441562 0.8473835
## Im8 0.8073195 0.7217525
## Im9 0.6249270 0.4559063
## Im10 0.8388964 0.8910746
## Im11 0.6909827 0.4449125
## Im12 0.8000487 0.8302990
## Im13 0.7632203 0.6999080
## Im14 0.8201246 0.8099945
## Im15 0.7087339 0.6317519
## Im16 0.7257516 0.4734149
## Im17 0.8553069 0.9223516
## Im18 0.8160203 0.7256024
## Im19 0.7158130 0.5297997
## Im20 0.8552184 0.7883146
## Im21 0.7951449 0.6494567
## Im22 0.8358300 0.7879817As expected, PCA often yields higher communalities estimates than PAF.
print(fa_pca_7f$loadings, cutoff=0.3, sort=TRUE)##
## Loadings:
## RC7 RC1 RC5 RC3 RC4 RC2 RC6
## Im8 0.716 0.497
## Im10 0.830
## Im14 0.808
## Im1 0.874
## Im2 0.890
## Im15 0.632 0.301
## Im3 0.830
## Im4 0.853
## Im5 0.813
## Im20 0.886
## Im21 0.835
## Im22 0.811
## Im11 0.776
## Im12 0.822
## Im13 0.751
## Im6 0.849
## Im7 0.375 0.814
## Im9 0.371 0.600
## Im17 0.780
## Im18 0.793
## Im19 0.438 0.399 0.502
## Im16 0.483 0.446 0.453
##
## RC7 RC1 RC5 RC3 RC4 RC2 RC6
## SS loadings 2.723 2.702 2.642 2.550 2.464 2.400 2.189
## Proportion Var 0.124 0.123 0.120 0.116 0.112 0.109 0.099
## Cumulative Var 0.124 0.247 0.367 0.483 0.595 0.704 0.803Same results from PAF . After implementing a 7-factor model, there are still some variables that have loadings on multiple factors such as lm 8,lm 16 and lm 19, thus we will try with 8 factors :
fa_pca_8f <- principal(
nfactors = 8,
image,
rotate="varimax",
scores=TRUE # If TRUE, find component scores
)
pca_communalities_8f <- data.frame(fa_pca_8f$communality,
fa_paf_8f$communality)
pca_communalities_8f## fa_pca_8f.communality fa_paf_8f.communality
## Im1 0.9238112 0.9324261
## Im2 0.9186596 0.8155382
## Im3 0.8851760 0.8559235
## Im4 0.9149950 0.9691025
## Im5 0.7946811 0.5764184
## Im6 0.8443973 0.7604978
## Im7 0.8561903 0.8474823
## Im8 0.8077646 0.7249609
## Im9 0.6580349 0.4555544
## Im10 0.9071324 0.8980931
## Im11 0.6910115 0.4457585
## Im12 0.8200642 0.8373341
## Im13 0.7659948 0.6993955
## Im14 0.9112282 0.8534420
## Im15 0.7363157 0.6464069
## Im16 0.8472172 0.7848879
## Im17 0.9050615 0.9053933
## Im18 0.9125390 0.7554077
## Im19 0.7846067 0.6245858
## Im20 0.8618400 0.8085432
## Im21 0.7976466 0.6464327
## Im22 0.8361820 0.7849973print(fa_pca_8f$loadings, cutoff=0.3, sort=TRUE)##
## Loadings:
## RC1 RC3 RC4 RC2 RC8 RC5 RC7 RC6
## Im3 0.822
## Im4 0.845
## Im5 0.814
## Im20 0.887
## Im21 0.835
## Im22 0.811
## Im11 0.768
## Im12 0.841
## Im13 0.758
## Im8 0.674 0.515
## Im10 0.883
## Im14 0.884
## Im6 0.870
## Im7 0.366 0.825
## Im9 0.388 0.635
## Im1 0.869
## Im2 0.891
## Im15 0.520 0.469
## Im16 0.822
## Im19 0.723
## Im17 0.807
## Im18 0.866
##
## RC1 RC3 RC4 RC2 RC8 RC5 RC7 RC6
## SS loadings 2.571 2.563 2.497 2.439 2.421 2.216 1.865 1.808
## Proportion Var 0.117 0.116 0.113 0.111 0.110 0.101 0.085 0.082
## Cumulative Var 0.117 0.233 0.347 0.458 0.568 0.669 0.753 0.8358-factor solution appears to be a good fit for our data. However, to further refine our results, we will re-do the analysis after removing variables 8,9 and 15 since they have low loading on two factors.
fa_pca_8f_n <- principal(
nfactors = 8,
image[,-c(8,9,15)],
rotate="varimax",
scores=TRUE # If TRUE, find component scores
)
pca_communalities_8f_n <- data.frame(fa_pca_8f_n$communality,
fa_paf_8f_n$communality)
pca_communalities_8f_n## fa_pca_8f_n.communality fa_paf_8f_n.communality
## Im1 0.9347185 0.9792472
## Im2 0.9354354 0.7782390
## Im3 0.8854065 0.8550184
## Im4 0.9169606 0.9682718
## Im5 0.7988686 0.5793745
## Im6 0.9142252 0.9011484
## Im7 0.8881899 0.7395077
## Im10 0.9365857 1.0096155
## Im11 0.6879301 0.4329273
## Im12 0.8412917 0.8670082
## Im13 0.7938506 0.6968226
## Im14 0.9194940 0.7737207
## Im16 0.8522562 0.6436939
## Im17 0.9087821 0.9643328
## Im18 0.9176481 0.7078105
## Im19 0.8203932 0.7275401
## Im20 0.8636520 0.8153635
## Im21 0.7900684 0.6382830
## Im22 0.8384857 0.7854382print(fa_pca_8f_n$loadings, cutoff=0.3, sort=TRUE)##
## Loadings:
## RC1 RC3 RC4 RC5 RC2 RC8 RC6 RC7
## Im3 0.827
## Im4 0.850
## Im5 0.818
## Im20 0.891
## Im21 0.833
## Im22 0.821
## Im11 0.758
## Im12 0.859
## Im13 0.781
## Im1 0.866
## Im2 0.892
## Im10 0.892
## Im14 0.869
## Im6 0.917
## Im7 0.309 0.859
## Im17 0.818
## Im18 0.876
## Im16 0.824
## Im19 0.751
##
## RC1 RC3 RC4 RC5 RC2 RC8 RC6 RC7
## SS loadings 2.556 2.525 2.334 1.881 1.875 1.843 1.786 1.645
## Proportion Var 0.135 0.133 0.123 0.099 0.099 0.097 0.094 0.087
## Cumulative Var 0.135 0.267 0.390 0.489 0.588 0.685 0.779 0.865Factors interpretation
What do GLB represent from your point of view? Large Assortment
What do GLB represent from your point of view? Assortment Variety
What do GLB represent from your point of view? Artistic Decoration of Sales Area
What do GLB represent from your point of view? Creative Decoration of Sales Area
What do GLB represent from your point of view? Appealing Arrangement of Shop Windows
What do GLB represent from your point of view? France
What do GLB represent from your point of view? French Savoir-vivre
What do GLB represent from your point of view? Expertise in French Traditional Cuisine
What do GLB represent from your point of view? French Fashion
What do GLB represent from your point of view? Gourmet Food
What do GLB represent from your point of view? High-quality Cosmetics
What do GLB represent from your point of view? Luxury brands
What do GLB represent from your point of view? Up to date Designer Brands
What do GLB represent from your point of view? Gourmet specialties
What do GLB represent from your point of view? Professional Selection of Brands
What do GLB represent from your point of view? Professional Appearance Towards Customers
What do GLB represent from your point of view? Are Trendy
What do GLB represent from your point of view? Are Hip
What do GLB represent from your point of view? Professional Organization
What do GLB represent from your point of view? Relaxing Shopping
What do GLB represent from your point of view? A Great Place to Stroll
What do GLB represent from your point of view? Intimate Shop Atmosphere
PFA
RC1 –> 3,4,5 –> Decoration
RC3 –> 20,21,22 –> Atmosphere or Ambiance
RC4 –> 11,12,13 –> Brand
RC5 -> 1,2 –> Variety
RC2 –> 10,14 –> Food or Cuisine
RC8 –> 6-7 –> Related to France
RC6 -> 17-18 ->Fashion or Mode
RC7 -> 16-19 ->Professionalism
PC
PA1 –> 3,4,5 –> Decoration
PA3 –> 20,21,22 –> Atmosphere or Ambiance
PA4 –> 11,12,13 –> Brand
PA5 -> 1,2 –> Variety
PA2 –> 10,14 –> Food or Cuisine
PA7 –> 6-7 –> Related to France
PA6 -> 17-18 ->Fashion or Mode
PA8 -> 16-19 ->Professionalism
Question 1
What are the dimensions by which Galeries Lafayette is perceived? Please explain your findings and rational for your final result.
Confirmatory Factor Analysis
model <- "
decoration=~ Im3+Im4+Im5
atmosphere=~ Im20+Im21+Im22
brand=~ Im11+Im12+Im13
variety=~ Im1 + Im2
cuisine=~ Im10+ Im14
france=~ Im6 + Im7
mode=~ Im17 + Im18
professionalism =~ Im16+ Im19"
fit <- cfa(model, myData, missing="ML")
summary(fit, fit.measures=TRUE,standardized=TRUE)## lavaan 0.6.15 ended normally after 107 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 85
##
## Number of observations 553
## Number of missing patterns 79
##
## Model Test User Model:
##
## Test statistic 259.047
## Degrees of freedom 124
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 7474.765
## Degrees of freedom 171
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.982
## Tucker-Lewis Index (TLI) 0.975
##
## Robust Comparative Fit Index (CFI) 0.981
## Robust Tucker-Lewis Index (TLI) 0.974
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12973.111
## Loglikelihood unrestricted model (H1) -12843.588
##
## Akaike (AIC) 26116.223
## Bayesian (BIC) 26483.028
## Sample-size adjusted Bayesian (SABIC) 26213.200
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.044
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.052
## P-value H_0: RMSEA <= 0.050 0.886
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.045
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.053
## P-value H_0: Robust RMSEA <= 0.050 0.825
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## decoration =~
## Im3 1.000 1.236 0.937
## Im4 1.056 0.025 42.716 0.000 1.305 0.969
## Im5 0.818 0.034 23.815 0.000 1.011 0.760
## atmosphere =~
## Im20 1.000 1.265 0.845
## Im21 0.849 0.041 20.823 0.000 1.074 0.783
## Im22 1.060 0.047 22.606 0.000 1.340 0.877
## brand =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.046 0.000 0.991 0.872
## Im13 1.465 0.105 13.968 0.000 1.030 0.855
## variety =~
## Im1 1.000 1.305 0.980
## Im2 0.885 0.033 27.043 0.000 1.155 0.899
## cuisine =~
## Im10 1.000 0.812 0.923
## Im14 1.015 0.036 28.479 0.000 0.824 0.952
## france =~
## Im6 1.000 0.975 0.813
## Im7 1.184 0.071 16.770 0.000 1.155 0.955
## mode =~
## Im17 1.000 1.204 0.969
## Im18 0.994 0.041 24.143 0.000 1.197 0.856
## professionalism =~
## Im16 1.000 0.921 0.766
## Im19 1.046 0.061 17.170 0.000 0.963 0.856
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## decoration ~~
## atmosphere 0.730 0.082 8.912 0.000 0.467 0.467
## brand 0.409 0.051 8.040 0.000 0.471 0.471
## variety 0.711 0.079 9.032 0.000 0.441 0.441
## cuisine 0.418 0.050 8.393 0.000 0.416 0.416
## france 0.402 0.063 6.350 0.000 0.334 0.334
## mode 0.770 0.076 10.140 0.000 0.517 0.517
## professionalsm 0.743 0.071 10.465 0.000 0.653 0.653
## atmosphere ~~
## brand 0.372 0.053 7.011 0.000 0.418 0.418
## variety 0.739 0.085 8.728 0.000 0.448 0.448
## cuisine 0.303 0.051 5.948 0.000 0.295 0.295
## france 0.410 0.065 6.352 0.000 0.333 0.333
## mode 0.787 0.081 9.715 0.000 0.516 0.516
## professionalsm 0.557 0.069 8.089 0.000 0.478 0.478
## brand ~~
## variety 0.439 0.054 8.161 0.000 0.478 0.478
## cuisine 0.258 0.034 7.662 0.000 0.452 0.452
## france 0.210 0.037 5.622 0.000 0.306 0.306
## mode 0.479 0.053 9.046 0.000 0.566 0.566
## professionalsm 0.343 0.043 7.946 0.000 0.529 0.529
## variety ~~
## cuisine 0.328 0.050 6.584 0.000 0.309 0.309
## france 0.286 0.060 4.735 0.000 0.225 0.225
## mode 0.817 0.079 10.362 0.000 0.519 0.519
## professionalsm 0.717 0.072 9.956 0.000 0.597 0.597
## cuisine ~~
## france 0.463 0.047 9.829 0.000 0.585 0.585
## mode 0.318 0.047 6.801 0.000 0.325 0.325
## professionalsm 0.372 0.043 8.589 0.000 0.498 0.498
## france ~~
## mode 0.378 0.061 6.175 0.000 0.322 0.322
## professionalsm 0.328 0.051 6.438 0.000 0.366 0.366
## mode ~~
## professionalsm 0.667 0.066 10.040 0.000 0.601 0.601
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.560 0.000 4.995 3.786
## .Im4 4.999 0.057 86.983 0.000 4.999 3.712
## .Im5 5.035 0.057 87.844 0.000 5.035 3.787
## .Im20 4.672 0.064 73.177 0.000 4.672 3.123
## .Im21 5.139 0.058 87.970 0.000 5.139 3.751
## .Im22 4.279 0.065 65.401 0.000 4.279 2.799
## .Im11 5.653 0.049 115.271 0.000 5.653 4.943
## .Im12 5.666 0.049 116.089 0.000 5.666 4.983
## .Im13 5.448 0.052 105.615 0.000 5.448 4.524
## .Im1 4.790 0.057 84.202 0.000 4.790 3.597
## .Im2 4.857 0.055 88.354 0.000 4.857 3.779
## .Im10 6.100 0.037 162.789 0.000 6.100 6.937
## .Im14 6.138 0.037 165.861 0.000 6.138 7.093
## .Im6 5.827 0.051 113.784 0.000 5.827 4.858
## .Im7 5.753 0.052 110.826 0.000 5.753 4.756
## .Im17 5.025 0.053 94.519 0.000 5.025 4.041
## .Im18 4.595 0.060 76.447 0.000 4.595 3.287
## .Im16 5.135 0.052 99.147 0.000 5.135 4.269
## .Im19 5.145 0.048 106.948 0.000 5.145 4.574
## decoration 0.000 0.000 0.000
## atmosphere 0.000 0.000 0.000
## brand 0.000 0.000 0.000
## variety 0.000 0.000 0.000
## cuisine 0.000 0.000 0.000
## france 0.000 0.000 0.000
## mode 0.000 0.000 0.000
## professionalsm 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.213 0.024 8.755 0.000 0.213 0.122
## .Im4 0.109 0.024 4.532 0.000 0.109 0.060
## .Im5 0.747 0.049 15.217 0.000 0.747 0.422
## .Im20 0.638 0.061 10.451 0.000 0.638 0.285
## .Im21 0.725 0.057 12.672 0.000 0.725 0.386
## .Im22 0.541 0.063 8.539 0.000 0.541 0.231
## .Im11 0.814 0.055 14.802 0.000 0.814 0.622
## .Im12 0.310 0.040 7.845 0.000 0.310 0.240
## .Im13 0.390 0.045 8.765 0.000 0.390 0.269
## .Im1 0.070 0.050 1.394 0.163 0.070 0.040
## .Im2 0.317 0.044 7.233 0.000 0.317 0.192
## .Im10 0.114 0.019 5.961 0.000 0.114 0.148
## .Im14 0.070 0.019 3.680 0.000 0.070 0.093
## .Im6 0.487 0.056 8.677 0.000 0.487 0.339
## .Im7 0.128 0.067 1.930 0.054 0.128 0.088
## .Im17 0.095 0.045 2.112 0.035 0.095 0.062
## .Im18 0.521 0.055 9.540 0.000 0.521 0.267
## .Im16 0.599 0.052 11.498 0.000 0.599 0.414
## .Im19 0.338 0.045 7.457 0.000 0.338 0.267
## decoration 1.528 0.107 14.326 0.000 1.000 1.000
## atmosphere 1.599 0.138 11.623 0.000 1.000 1.000
## brand 0.494 0.067 7.361 0.000 1.000 1.000
## variety 1.704 0.118 14.388 0.000 1.000 1.000
## cuisine 0.659 0.049 13.328 0.000 1.000 1.000
## france 0.952 0.095 10.058 0.000 1.000 1.000
## mode 1.451 0.104 13.988 0.000 1.000 1.000
## professionalsm 0.849 0.088 9.638 0.000 1.000 1.000Results
To evaluate whether our model is good or not, we will check the fit measures. The first global fit measure we will consider is the Chi-squared test. According to slide 68 of our course, a low Chi2-value (considering degrees of freedom) indicates a good fit, and the ratio of Chi2-value/df should be below 5 for samples up to 1000. Since we have 553 observations, we calculate the ratio as 259.047/124 = 2.089089, which is below 5. Therefore, our Chi-squared test result is good.
Moving on to the second fit measure, according to slide 69 of our course, we need a Root Mean Square Error of Approximation (RMSEA) below 0.05 to have a good model. In our case, the RMSEA is 0.044, and the robust RMSEA is 0.045, indicating that we have a good model.
Finally, we will check the Comparative Fit Index (CFI) which is the last fit measure from slide 70 of our course. A CFI above 0.95 indicates a good model. In our case, we have a CFI of 0.982, which is above the required threshold, indicating a good model.
Based on these fit measures, we can conclude that our factor analysis was good for our model.
parameterestimates(fit, boot.ci.type = "bca.simple", standardized = TRUE)%>% kable()| lhs | op | rhs | est | se | z | pvalue | ci.lower | ci.upper | std.lv | std.all | std.nox |
|---|---|---|---|---|---|---|---|---|---|---|---|
| decoration | =~ | Im3 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 1.2359656 | 0.9367725 | 0.9367725 |
| decoration | =~ | Im4 | 1.0562183 | 0.0247262 | 42.716500 | 0.0000000 | 1.0077558 | 1.1046808 | 1.3054495 | 0.9694446 | 0.9694446 |
| decoration | =~ | Im5 | 0.8178299 | 0.0343414 | 23.814727 | 0.0000000 | 0.7505221 | 0.8851377 | 1.0108096 | 0.7601410 | 0.7601410 |
| atmosphere | =~ | Im20 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 1.2646012 | 0.8453892 | 0.8453892 |
| atmosphere | =~ | Im21 | 0.8489179 | 0.0407673 | 20.823486 | 0.0000000 | 0.7690154 | 0.9288204 | 1.0735425 | 0.7834328 | 0.7834328 |
| atmosphere | =~ | Im22 | 1.0598950 | 0.0468851 | 22.606229 | 0.0000000 | 0.9680019 | 1.1517881 | 1.3403445 | 0.8767075 | 0.8767075 |
| brand | =~ | Im11 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 0.7029587 | 0.6145742 | 0.6145742 |
| brand | =~ | Im12 | 1.4102158 | 0.0937252 | 15.046288 | 0.0000000 | 1.2265179 | 1.5939138 | 0.9913235 | 0.8719186 | 0.8719186 |
| brand | =~ | Im13 | 1.4646567 | 0.1048551 | 13.968386 | 0.0000000 | 1.2591445 | 1.6701690 | 1.0295932 | 0.8549780 | 0.8549780 |
| variety | =~ | Im1 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 1.3052701 | 0.9800185 | 0.9800185 |
| variety | =~ | Im2 | 0.8851714 | 0.0327322 | 27.042813 | 0.0000000 | 0.8210174 | 0.9493254 | 1.1553878 | 0.8989149 | 0.8989149 |
| cuisine | =~ | Im10 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 0.8117871 | 0.9231434 | 0.9231434 |
| cuisine | =~ | Im14 | 1.0152003 | 0.0356474 | 28.478940 | 0.0000000 | 0.9453327 | 1.0850680 | 0.8241265 | 0.9523888 | 0.9523888 |
| france | =~ | Im6 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 0.9754586 | 0.8131642 | 0.8131642 |
| france | =~ | Im7 | 1.1842984 | 0.0706189 | 16.770282 | 0.0000000 | 1.0458880 | 1.3227089 | 1.1552341 | 0.9550804 | 0.9550804 |
| mode | =~ | Im17 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 1.2044990 | 0.9687196 | 0.9687196 |
| mode | =~ | Im18 | 0.9938483 | 0.0411645 | 24.143323 | 0.0000000 | 0.9131673 | 1.0745293 | 1.1970892 | 0.8563450 | 0.8563450 |
| professionalism | =~ | Im16 | 1.0000000 | 0.0000000 | NA | NA | 1.0000000 | 1.0000000 | 0.9213055 | 0.7658145 | 0.7658145 |
| professionalism | =~ | Im19 | 1.0455259 | 0.0608933 | 17.169812 | 0.0000000 | 0.9261773 | 1.1648745 | 0.9632488 | 0.8562871 | 0.8562871 |
| Im3 | ~~ | Im3 | 0.2131716 | 0.0243487 | 8.754934 | 0.0000000 | 0.1654489 | 0.2608942 | 0.2131716 | 0.1224573 | 0.1224573 |
| Im4 | ~~ | Im4 | 0.1091203 | 0.0240777 | 4.532002 | 0.0000058 | 0.0619288 | 0.1563117 | 0.1091203 | 0.0601771 | 0.0601771 |
| Im5 | ~~ | Im5 | 0.7465416 | 0.0490606 | 15.216713 | 0.0000000 | 0.6503845 | 0.8426986 | 0.7465416 | 0.4221857 | 0.4221857 |
| Im20 | ~~ | Im20 | 0.6384421 | 0.0610890 | 10.451013 | 0.0000000 | 0.5187098 | 0.7581744 | 0.6384421 | 0.2853171 | 0.2853171 |
| Im21 | ~~ | Im21 | 0.7252447 | 0.0572326 | 12.671876 | 0.0000000 | 0.6130708 | 0.8374186 | 0.7252447 | 0.3862331 | 0.3862331 |
| Im22 | ~~ | Im22 | 0.5408251 | 0.0633323 | 8.539482 | 0.0000000 | 0.4166961 | 0.6649542 | 0.5408251 | 0.2313840 | 0.2313840 |
| Im11 | ~~ | Im11 | 0.8141599 | 0.0550047 | 14.801638 | 0.0000000 | 0.7063526 | 0.9219671 | 0.8141599 | 0.6222985 | 0.6222985 |
| Im12 | ~~ | Im12 | 0.3099218 | 0.0395081 | 7.844518 | 0.0000000 | 0.2324874 | 0.3873562 | 0.3099218 | 0.2397580 | 0.2397580 |
| Im13 | ~~ | Im13 | 0.3901163 | 0.0445070 | 8.765285 | 0.0000000 | 0.3028842 | 0.4773483 | 0.3901163 | 0.2690126 | 0.2690126 |
| Im1 | ~~ | Im1 | 0.0701827 | 0.0503511 | 1.393865 | 0.1633584 | -0.0285037 | 0.1688690 | 0.0701827 | 0.0395638 | 0.0395638 |
| Im2 | ~~ | Im2 | 0.3171108 | 0.0438406 | 7.233265 | 0.0000000 | 0.2311848 | 0.4030369 | 0.3171108 | 0.1919520 | 0.1919520 |
| Im10 | ~~ | Im10 | 0.1142980 | 0.0191756 | 5.960607 | 0.0000000 | 0.0767146 | 0.1518814 | 0.1142980 | 0.1478062 | 0.1478062 |
| Im14 | ~~ | Im14 | 0.0696040 | 0.0189122 | 3.680371 | 0.0002329 | 0.0325367 | 0.1066713 | 0.0696040 | 0.0929555 | 0.0929555 |
| Im6 | ~~ | Im6 | 0.4874817 | 0.0561797 | 8.677186 | 0.0000000 | 0.3773715 | 0.5975919 | 0.4874817 | 0.3387640 | 0.3387640 |
| Im7 | ~~ | Im7 | 0.1284875 | 0.0665897 | 1.929539 | 0.0536640 | -0.0020260 | 0.2590010 | 0.1284875 | 0.0878215 | 0.0878215 |
| Im17 | ~~ | Im17 | 0.0952080 | 0.0450825 | 2.111862 | 0.0346983 | 0.0068480 | 0.1835680 | 0.0952080 | 0.0615824 | 0.0615824 |
| Im18 | ~~ | Im18 | 0.5211167 | 0.0546249 | 9.539915 | 0.0000000 | 0.4140539 | 0.6281795 | 0.5211167 | 0.2666733 | 0.2666733 |
| Im16 | ~~ | Im16 | 0.5985014 | 0.0520508 | 11.498406 | 0.0000000 | 0.4964837 | 0.7005191 | 0.5985014 | 0.4135281 | 0.4135281 |
| Im19 | ~~ | Im19 | 0.3375819 | 0.0452691 | 7.457218 | 0.0000000 | 0.2488560 | 0.4263078 | 0.3375819 | 0.2667725 | 0.2667725 |
| decoration | ~~ | decoration | 1.5276110 | 0.1066312 | 14.326121 | 0.0000000 | 1.3186177 | 1.7366042 | 1.0000000 | 1.0000000 | 1.0000000 |
| atmosphere | ~~ | atmosphere | 1.5992161 | 0.1375961 | 11.622538 | 0.0000000 | 1.3295327 | 1.8688995 | 1.0000000 | 1.0000000 | 1.0000000 |
| brand | ~~ | brand | 0.4941509 | 0.0671291 | 7.361201 | 0.0000000 | 0.3625803 | 0.6257216 | 1.0000000 | 1.0000000 | 1.0000000 |
| variety | ~~ | variety | 1.7037299 | 0.1184131 | 14.388014 | 0.0000000 | 1.4716444 | 1.9358154 | 1.0000000 | 1.0000000 | 1.0000000 |
| cuisine | ~~ | cuisine | 0.6589982 | 0.0494455 | 13.327778 | 0.0000000 | 0.5620869 | 0.7559096 | 1.0000000 | 1.0000000 | 1.0000000 |
| france | ~~ | france | 0.9515194 | 0.0946007 | 10.058276 | 0.0000000 | 0.7661056 | 1.1369333 | 1.0000000 | 1.0000000 | 1.0000000 |
| mode | ~~ | mode | 1.4508177 | 0.1037220 | 13.987562 | 0.0000000 | 1.2475264 | 1.6541091 | 1.0000000 | 1.0000000 | 1.0000000 |
| professionalism | ~~ | professionalism | 0.8488038 | 0.0880708 | 9.637738 | 0.0000000 | 0.6761881 | 1.0214194 | 1.0000000 | 1.0000000 | 1.0000000 |
| decoration | ~~ | atmosphere | 0.7297103 | 0.0818788 | 8.912084 | 0.0000000 | 0.5692309 | 0.8901897 | 0.4668641 | 0.4668641 | 0.4668641 |
| decoration | ~~ | brand | 0.4092289 | 0.0508965 | 8.040419 | 0.0000000 | 0.3094737 | 0.5089842 | 0.4710100 | 0.4710100 | 0.4710100 |
| decoration | ~~ | variety | 0.7107783 | 0.0786918 | 9.032435 | 0.0000000 | 0.5565452 | 0.8650113 | 0.4405826 | 0.4405826 | 0.4405826 |
| decoration | ~~ | cuisine | 0.4178485 | 0.0497850 | 8.393057 | 0.0000000 | 0.3202716 | 0.5154253 | 0.4164571 | 0.4164571 | 0.4164571 |
| decoration | ~~ | france | 0.4023560 | 0.0633605 | 6.350269 | 0.0000000 | 0.2781718 | 0.5265403 | 0.3337300 | 0.3337300 | 0.3337300 |
| decoration | ~~ | mode | 0.7699775 | 0.0759369 | 10.139703 | 0.0000000 | 0.6211439 | 0.9188110 | 0.5172080 | 0.5172080 | 0.5172080 |
| decoration | ~~ | professionalism | 0.7434486 | 0.0710411 | 10.465043 | 0.0000000 | 0.6042106 | 0.8826867 | 0.6528914 | 0.6528914 | 0.6528914 |
| atmosphere | ~~ | brand | 0.3718641 | 0.0530375 | 7.011348 | 0.0000000 | 0.2679126 | 0.4758156 | 0.4183126 | 0.4183126 | 0.4183126 |
| atmosphere | ~~ | variety | 0.7394490 | 0.0847246 | 8.727682 | 0.0000000 | 0.5733919 | 0.9055061 | 0.4479755 | 0.4479755 | 0.4479755 |
| atmosphere | ~~ | cuisine | 0.3026751 | 0.0508836 | 5.948386 | 0.0000000 | 0.2029451 | 0.4024051 | 0.2948363 | 0.2948363 | 0.2948363 |
| atmosphere | ~~ | france | 0.4102130 | 0.0645828 | 6.351736 | 0.0000000 | 0.2836330 | 0.5367930 | 0.3325424 | 0.3325424 | 0.3325424 |
| atmosphere | ~~ | mode | 0.7866627 | 0.0809721 | 9.715233 | 0.0000000 | 0.6279603 | 0.9453650 | 0.5164503 | 0.5164503 | 0.5164503 |
| atmosphere | ~~ | professionalism | 0.5567716 | 0.0688297 | 8.089122 | 0.0000000 | 0.4218679 | 0.6916753 | 0.4778811 | 0.4778811 | 0.4778811 |
| brand | ~~ | variety | 0.4385490 | 0.0537367 | 8.161069 | 0.0000000 | 0.3332270 | 0.5438710 | 0.4779560 | 0.4779560 | 0.4779560 |
| brand | ~~ | cuisine | 0.2581081 | 0.0336849 | 7.662427 | 0.0000000 | 0.1920869 | 0.3241292 | 0.4523032 | 0.4523032 | 0.4523032 |
| brand | ~~ | france | 0.2095183 | 0.0372700 | 5.621629 | 0.0000000 | 0.1364704 | 0.2825662 | 0.3055507 | 0.3055507 | 0.3055507 |
| brand | ~~ | mode | 0.4794807 | 0.0530033 | 9.046244 | 0.0000000 | 0.3755962 | 0.5833653 | 0.5662848 | 0.5662848 | 0.5662848 |
| brand | ~~ | professionalism | 0.3426340 | 0.0431207 | 7.945934 | 0.0000000 | 0.2581190 | 0.4271489 | 0.5290503 | 0.5290503 | 0.5290503 |
| variety | ~~ | cuisine | 0.3278522 | 0.0497940 | 6.584167 | 0.0000000 | 0.2302577 | 0.4254467 | 0.3094109 | 0.3094109 | 0.3094109 |
| variety | ~~ | france | 0.2864239 | 0.0604918 | 4.734924 | 0.0000022 | 0.1678622 | 0.4049856 | 0.2249573 | 0.2249573 | 0.2249573 |
| variety | ~~ | mode | 0.8166276 | 0.0788081 | 10.362234 | 0.0000000 | 0.6621666 | 0.9710885 | 0.5194183 | 0.5194183 | 0.5194183 |
| variety | ~~ | professionalism | 0.7174390 | 0.0720626 | 9.955777 | 0.0000000 | 0.5761989 | 0.8586790 | 0.5965968 | 0.5965968 | 0.5965968 |
| cuisine | ~~ | france | 0.4634995 | 0.0471579 | 9.828681 | 0.0000000 | 0.3710718 | 0.5559272 | 0.5853266 | 0.5853266 | 0.5853266 |
| cuisine | ~~ | mode | 0.3180388 | 0.0467609 | 6.801386 | 0.0000000 | 0.2263892 | 0.4096885 | 0.3252607 | 0.3252607 | 0.3252607 |
| cuisine | ~~ | professionalism | 0.3722167 | 0.0433381 | 8.588667 | 0.0000000 | 0.2872756 | 0.4571579 | 0.4976799 | 0.4976799 | 0.4976799 |
| france | ~~ | mode | 0.3781934 | 0.0612427 | 6.175317 | 0.0000000 | 0.2581598 | 0.4982270 | 0.3218835 | 0.3218835 | 0.3218835 |
| france | ~~ | professionalism | 0.3284956 | 0.0510209 | 6.438446 | 0.0000000 | 0.2284964 | 0.4284948 | 0.3655250 | 0.3655250 | 0.3655250 |
| mode | ~~ | professionalism | 0.6665756 | 0.0663933 | 10.039803 | 0.0000000 | 0.5364472 | 0.7967041 | 0.6006747 | 0.6006747 | 0.6006747 |
| Im3 | ~1 | 4.9951357 | 0.0564037 | 88.560425 | 0.0000000 | 4.8845865 | 5.1056850 | 4.9951357 | 3.7859514 | 3.7859514 | |
| Im4 | ~1 | 4.9985357 | 0.0574659 | 86.982685 | 0.0000000 | 4.8859047 | 5.1111668 | 4.9985357 | 3.7119809 | 3.7119809 | |
| Im5 | ~1 | 5.0354361 | 0.0573222 | 87.844461 | 0.0000000 | 4.9230867 | 5.1477855 | 5.0354361 | 3.7867084 | 3.7867084 | |
| Im20 | ~1 | 4.6721297 | 0.0638470 | 73.176928 | 0.0000000 | 4.5469918 | 4.7972675 | 4.6721297 | 3.1233310 | 3.1233310 | |
| Im21 | ~1 | 5.1393791 | 0.0584218 | 87.970159 | 0.0000000 | 5.0248744 | 5.2538838 | 5.1393791 | 3.7505341 | 3.7505341 | |
| Im22 | ~1 | 4.2788656 | 0.0654246 | 65.401448 | 0.0000000 | 4.1506357 | 4.4070955 | 4.2788656 | 2.7987681 | 2.7987681 | |
| Im11 | ~1 | 5.6533330 | 0.0490440 | 115.270730 | 0.0000000 | 5.5572086 | 5.7494574 | 5.6533330 | 4.9425276 | 4.9425276 | |
| Im12 | ~1 | 5.6655222 | 0.0488034 | 116.088770 | 0.0000000 | 5.5698693 | 5.7611750 | 5.6655222 | 4.9831101 | 4.9831101 | |
| Im13 | ~1 | 5.4481356 | 0.0515847 | 105.615358 | 0.0000000 | 5.3470314 | 5.5492397 | 5.4481356 | 4.5241521 | 4.5241521 | |
| Im1 | ~1 | 4.7904479 | 0.0568921 | 84.202388 | 0.0000000 | 4.6789415 | 4.9019544 | 4.7904479 | 3.5967481 | 3.5967481 | |
| Im2 | ~1 | 4.8567638 | 0.0549691 | 88.354396 | 0.0000000 | 4.7490262 | 4.9645013 | 4.8567638 | 3.7786598 | 3.7786598 | |
| Im10 | ~1 | 6.0998164 | 0.0374707 | 162.788945 | 0.0000000 | 6.0263752 | 6.1732576 | 6.0998164 | 6.9365548 | 6.9365548 | |
| Im14 | ~1 | 6.1379973 | 0.0370068 | 165.861320 | 0.0000000 | 6.0654653 | 6.2105293 | 6.1379973 | 7.0932802 | 7.0932802 | |
| Im6 | ~1 | 5.8271294 | 0.0512121 | 113.784210 | 0.0000000 | 5.7267555 | 5.9275033 | 5.8271294 | 4.8576261 | 4.8576261 | |
| Im7 | ~1 | 5.7528798 | 0.0519089 | 110.826392 | 0.0000000 | 5.6511401 | 5.8546194 | 5.7528798 | 4.7561466 | 4.7561466 | |
| Im17 | ~1 | 5.0245978 | 0.0531596 | 94.519090 | 0.0000000 | 4.9204069 | 5.1287887 | 5.0245978 | 4.0410381 | 4.0410381 | |
| Im18 | ~1 | 4.5945802 | 0.0601017 | 76.446719 | 0.0000000 | 4.4767829 | 4.7123774 | 4.5945802 | 3.2867606 | 3.2867606 | |
| Im16 | ~1 | 5.1353964 | 0.0517956 | 99.147426 | 0.0000000 | 5.0338790 | 5.2369138 | 5.1353964 | 4.2686831 | 4.2686831 | |
| Im19 | ~1 | 5.1451102 | 0.0481086 | 106.947872 | 0.0000000 | 5.0508191 | 5.2394013 | 5.1451102 | 4.5737835 | 4.5737835 | |
| decoration | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| atmosphere | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| brand | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| variety | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| cuisine | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| france | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| mode | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | |
| professionalism | ~1 | 0.0000000 | 0.0000000 | NA | NA | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
We can observe that all values are significant. During class, we learned that upper and lower case should not include 0, except for IM 1 and IM 7 in relation to themselves. Despite this exception, the results are still satisfactory.
#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im3,Im4,Im5)))
CronReli## $sample.size
## [1] 508
##
## $number.of.items
## [1] 3
##
## $alpha
## [1] 0.9151505#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im20,Im21,Im22)))
CronReli## $sample.size
## [1] 525
##
## $number.of.items
## [1] 3
##
## $alpha
## [1] 0.8749604#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im11,Im12,Im13)))
CronReli## $sample.size
## [1] 520
##
## $number.of.items
## [1] 3
##
## $alpha
## [1] 0.8127499#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im1,Im2)))
CronReli## $sample.size
## [1] 525
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.9372013#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im10,Im14)))
CronReli## $sample.size
## [1] 525
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.9334071#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im6,Im7)))
CronReli## $sample.size
## [1] 520
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.8758912#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im17,Im18)))
CronReli## $sample.size
## [1] 521
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.9039139#calculating reliability
CronReli=cronbach(subset(myData, select = c(Im16,Im19)))
CronReli## $sample.size
## [1] 520
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.7940545All of Cronbach’s alpha greater than 0.7 indicating that the observed variables have sufficient reliability
std_fit=inspect(fit, "std")
std_fit$psi## decrtn atmsph brand varity cuisin france mode prfssn
## decoration 1.000
## atmosphere 0.467 1.000
## brand 0.471 0.418 1.000
## variety 0.441 0.448 0.478 1.000
## cuisine 0.416 0.295 0.452 0.309 1.000
## france 0.334 0.333 0.306 0.225 0.585 1.000
## mode 0.517 0.516 0.566 0.519 0.325 0.322 1.000
## professionalism 0.653 0.478 0.529 0.597 0.498 0.366 0.601 1.000some comment on covariances include:
decoration and professionalism (0.653): This suggests a strong positive relationship between these two factors, meaning that as the decoration quality increases, professionalism is also likely to increase.
cuisine and atmosphere (0.295): This suggests a relatively weak positive relationship between these two factors, meaning that the quality of the cuisine is not strongly related to the atmosphere of the establishment.
std_fit$lambda## decrtn atmsph brand varity cuisin france mode prfssn
## Im3 0.937 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im4 0.969 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im5 0.760 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im20 0.000 0.845 0.000 0.000 0.000 0.000 0.000 0.000
## Im21 0.000 0.783 0.000 0.000 0.000 0.000 0.000 0.000
## Im22 0.000 0.877 0.000 0.000 0.000 0.000 0.000 0.000
## Im11 0.000 0.000 0.615 0.000 0.000 0.000 0.000 0.000
## Im12 0.000 0.000 0.872 0.000 0.000 0.000 0.000 0.000
## Im13 0.000 0.000 0.855 0.000 0.000 0.000 0.000 0.000
## Im1 0.000 0.000 0.000 0.980 0.000 0.000 0.000 0.000
## Im2 0.000 0.000 0.000 0.899 0.000 0.000 0.000 0.000
## Im10 0.000 0.000 0.000 0.000 0.923 0.000 0.000 0.000
## Im14 0.000 0.000 0.000 0.000 0.952 0.000 0.000 0.000
## Im6 0.000 0.000 0.000 0.000 0.000 0.813 0.000 0.000
## Im7 0.000 0.000 0.000 0.000 0.000 0.955 0.000 0.000
## Im17 0.000 0.000 0.000 0.000 0.000 0.000 0.969 0.000
## Im18 0.000 0.000 0.000 0.000 0.000 0.000 0.856 0.000
## Im16 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.766
## Im19 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.856Each construct has loadings greater than 0.7 except for Im11, indicating that at least 50% of the variance in each indicator is explained by the underlying construct.
std_fit$theta## Im3 Im4 Im5 Im20 Im21 Im22 Im11 Im12 Im13 Im1 Im2 Im10
## Im3 0.122
## Im4 0.000 0.060
## Im5 0.000 0.000 0.422
## Im20 0.000 0.000 0.000 0.285
## Im21 0.000 0.000 0.000 0.000 0.386
## Im22 0.000 0.000 0.000 0.000 0.000 0.231
## Im11 0.000 0.000 0.000 0.000 0.000 0.000 0.622
## Im12 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.240
## Im13 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.269
## Im1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.040
## Im2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.192
## Im10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.148
## Im14 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im17 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im18 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im16 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im19 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im14 Im6 Im7 Im17 Im18 Im16 Im19
## Im3
## Im4
## Im5
## Im20
## Im21
## Im22
## Im11
## Im12
## Im13
## Im1
## Im2
## Im10
## Im14 0.093
## Im6 0.000 0.339
## Im7 0.000 0.000 0.088
## Im17 0.000 0.000 0.000 0.062
## Im18 0.000 0.000 0.000 0.000 0.267
## Im16 0.000 0.000 0.000 0.000 0.000 0.414
## Im19 0.000 0.000 0.000 0.000 0.000 0.000 0.267From theta matrix we can see that the diagonal values range from 0.040(IM1) to 0.622(Im11). Lower values indicate that the latent factors account for a larger proportion of the variance in the observed variables, while higher values suggest that the latent factors explain less of the variance in the observed variables
modificationindices(fit) %>% filter(mi>10)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 atmosphere =~ Im12 10.952 -0.115 -0.145 -0.127 -0.127
## 2 variety =~ Im20 14.777 -0.151 -0.197 -0.132 -0.132
## 3 variety =~ Im12 10.663 -0.111 -0.145 -0.127 -0.127
## 4 variety =~ Im13 13.970 0.133 0.174 0.144 0.144
## 5 cuisine =~ Im11 12.742 0.215 0.174 0.152 0.152
## 6 mode =~ Im12 17.245 -0.179 -0.216 -0.190 -0.190
## 7 mode =~ Im13 23.832 0.220 0.265 0.220 0.220
## 8 Im20 ~~ Im21 11.455 0.228 0.228 0.335 0.335
## 9 Im21 ~~ Im22 15.140 -0.285 -0.285 -0.455 -0.455
## 10 Im11 ~~ Im12 13.307 0.145 0.145 0.288 0.288
## 11 Im11 ~~ Im13 21.323 -0.191 -0.191 -0.338 -0.338
## 12 Im13 ~~ Im1 10.708 0.068 0.068 0.409 0.409Since we do not have a Large Modification Indices (mi) that indicate that we have a good model.
Question 2
Are the mechanism driving satisfaction and affective commitment similar? Are satisfaction and affective commitment mediating the impact of image perceptions on outcomes? If yes for which outcomes?
To create a structural equation model, we need to consider the relationships between the observed variables and latent variables based on the known structure:
Images → Mediators → Outcomes
For this model, we have:
Images: The 8 dimensions found previously.
Mediators: Affective Commitment (with COM_A1 – COM_A4) and Customer Satisfaction (with SAT_1 – SAT_3).
Outcomes: Repurchase Intention (with C_REP1 – C_REP3) and Co-creation (with C_CR1, C_CR3, C_CR4).
Now let’s define the model:
Images: These are the 8 dimensions we identified earlier, which serve as the predictor variables in our model.
Mediators:
Affective Commitment (AC) =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
Customer Satisfaction (CS) =~ SAT_1 + SAT_2 + SAT_3
Outcomes:
Repurchase Intention (RI) =~ C_REP1 + C_REP2 + C_REP3
Co-creation (CC) =~ C_CR1 + C_CR3 + C_CR4
Model
model1 <- "
# measurement model (=~)
decoration=~ Im3+Im4+Im5
atmosphere=~ Im20+Im21+Im22
brand=~ Im11+Im12+Im13
variety=~ Im1 + Im2
cuisine=~ Im10+ Im14
france=~ Im6 + Im7
mode=~ Im17 + Im18
professionalism =~ Im16+ Im19
satisfaction =~ SAT_1 + SAT_2 + SAT_3
commitment =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
cocreation =~ C_CR1 + C_CR3 + C_CR4
repurchase =~ C_REP1 + C_REP2 + C_REP3
# Structural model ( ~)
cocreation ~ a * satisfaction + b * commitment
repurchase ~ c * satisfaction + d * commitment
satisfaction ~ e * professionalism + f * mode + g * france + h * cuisine + i * variety + j * brand + k * atmosphere + l * decoration
commitment ~ m * professionalism + n * mode + o * france + p * cuisine + q * variety + r * brand + s * atmosphere + t * decoration
cocreation ~ u * professionalism + v * mode + w * france + x * cuisine + y * variety + z * brand+ aa * atmosphere + bb * decoration
repurchase ~ cc * professionalism + dd * mode + ee * france + ff * cuisine + gg * variety + hh * brand + ii * atmosphere + jj * decoration
# indirect effect (:=)
# for cocreation:
ae:=a*e
af:=a*f
ag:=a*g
ah:=a*h
ai:=a*i
aj:=a*j
ak:=a*k
al:=a*l
bm:=b*m
bn:=b*n
bo:=b*o
bp:=b*p
bq:=b*q
br:=b*r
bs:=b*s
bt:=b*t
# for repurchase
ce:=c*e
cf:=c*f
cg:=c*g
ch:=c*h
ci:=c*i
cj:=c*j
ck:=c*k
cl:=c*l
dm:=d*m
dn:=d*n
do:=d*o
dp:=d*p
dq:=d*q
dr:=d*r
ds:=d*s
dt:=d*t
# Total effects ( := TE)
# for cocreation
TE1C:= u + (a*e) + (b*m)
TE2C:= v + (a*f) + (b*n)
TE3C:= w + (a*g) + (b*o)
TE4C:= x + (a*h) + (b*p)
TE5C:= y + (a*i) + (b*q)
TE6C:= z + (a*j) + (b*r)
TE7C:= aa + (a*k) + (b*s)
TE8C:= bb + (a*l) + (b*t)
# for repurchase
TE1R:= cc + (c*e) + (d*m)
TE2R:= dd + (c*f) + (d*n)
TE3R:= ee + (c*g) + (d*o)
TE4R:= ff + (c*h) + (d*p)
TE5R:= gg + (c*i) + (d*q)
TE6R:= hh + (c*j) + (d*r)
TE7R:= ii + (c*k) + (d*s)
TE8R:= jj + (c*l) + (d*t)
# total indirect effect
# for cocreation
TIE1C:= (a*e) + (b*m)
TIE2C:= (a*f) + (b*n)
TIE3C:= (a*g) + (b*o)
TIE4C:= (a*h) + (b*p)
TIE5C:= (a*i) + (b*q)
TIE6C:= (a*j) + (b*r)
TIE7C:= (a*k) + (b*s)
TIE8C:= (a*l) + (b*t)
# for repurchase
TIE1R:= (c*e) + (d*m)
TIE2R:= (c*f) + (d*n)
TIE3R:= (c*g) + (d*o)
TIE4R:= (c*h) + (d*p)
TIE5R:= (c*i) + (d*q)
TIE6R:= (c*j) + (d*r)
TIE7R:= (c*k) + (d*s)
TIE8R:= (c*l) + (d*t)
"
fit1<-cfa(model1, data=myData,estimator="MLR", missing="ML")
summary(fit1, fit.measures=TRUE,standardized=TRUE)## lavaan 0.6.15 ended normally after 149 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 161
##
## Number of observations 553
## Number of missing patterns 135
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 700.455 632.247
## Degrees of freedom 399 399
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.108
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 11978.557 9969.592
## Degrees of freedom 496 496
## P-value 0.000 0.000
## Scaling correction factor 1.202
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.974 0.975
## Tucker-Lewis Index (TLI) 0.967 0.969
##
## Robust Comparative Fit Index (CFI) 0.979
## Robust Tucker-Lewis Index (TLI) 0.973
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -22368.900 -22368.900
## Scaling correction factor 1.404
## for the MLR correction
## Loglikelihood unrestricted model (H1) -22018.673 -22018.673
## Scaling correction factor 1.193
## for the MLR correction
##
## Akaike (AIC) 45059.800 45059.800
## Bayesian (BIC) 45754.573 45754.573
## Sample-size adjusted Bayesian (SABIC) 45243.488 45243.488
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.037 0.033
## 90 Percent confidence interval - lower 0.032 0.028
## 90 Percent confidence interval - upper 0.041 0.037
## P-value H_0: RMSEA <= 0.050 1.000 1.000
## P-value H_0: RMSEA >= 0.080 0.000 0.000
##
## Robust RMSEA 0.034
## 90 Percent confidence interval - lower 0.029
## 90 Percent confidence interval - upper 0.039
## P-value H_0: Robust RMSEA <= 0.050 1.000
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.041 0.041
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## decoration =~
## Im3 1.000 1.235 0.936
## Im4 1.057 0.028 37.421 0.000 1.306 0.970
## Im5 0.818 0.046 17.727 0.000 1.011 0.760
## atmosphere =~
## Im20 1.000 1.262 0.844
## Im21 0.857 0.046 18.667 0.000 1.081 0.789
## Im22 1.056 0.048 21.798 0.000 1.333 0.873
## brand =~
## Im11 1.000 0.701 0.613
## Im12 1.414 0.113 12.568 0.000 0.991 0.872
## Im13 1.468 0.140 10.474 0.000 1.029 0.855
## variety =~
## Im1 1.000 1.297 0.974
## Im2 0.896 0.035 25.253 0.000 1.162 0.904
## cuisine =~
## Im10 1.000 0.810 0.921
## Im14 1.021 0.041 24.871 0.000 0.827 0.955
## france =~
## Im6 1.000 0.987 0.822
## Im7 1.158 0.076 15.174 0.000 1.143 0.944
## mode =~
## Im17 1.000 1.205 0.970
## Im18 0.992 0.042 23.744 0.000 1.196 0.855
## professionalism =~
## Im16 1.000 0.919 0.764
## Im19 1.043 0.071 14.680 0.000 0.959 0.853
## satisfaction =~
## SAT_1 1.000 0.882 0.865
## SAT_2 0.933 0.059 15.698 0.000 0.823 0.819
## SAT_3 0.809 0.061 13.271 0.000 0.714 0.624
## commitment =~
## COM_A1 1.000 1.144 0.796
## COM_A2 1.174 0.049 23.795 0.000 1.342 0.836
## COM_A3 1.162 0.059 19.802 0.000 1.329 0.817
## COM_A4 1.278 0.064 20.041 0.000 1.462 0.842
## cocreation =~
## C_CR1 1.000 1.658 0.851
## C_CR3 1.033 0.056 18.597 0.000 1.712 0.826
## C_CR4 0.963 0.056 17.089 0.000 1.597 0.806
## repurchase =~
## C_REP1 1.000 0.596 0.816
## C_REP2 0.971 0.048 20.251 0.000 0.579 0.931
## C_REP3 0.702 0.057 12.368 0.000 0.419 0.756
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cocreation ~
## satisfctn (a) -0.357 0.143 -2.501 0.012 -0.190 -0.190
## commitmnt (b) 0.546 0.094 5.824 0.000 0.377 0.377
## repurchase ~
## satisfctn (c) 0.215 0.049 4.396 0.000 0.318 0.318
## commitmnt (d) 0.184 0.031 5.882 0.000 0.354 0.354
## satisfaction ~
## prfssnlsm (e) 0.459 0.105 4.382 0.000 0.479 0.479
## mode (f) 0.008 0.061 0.131 0.896 0.011 0.011
## france (g) 0.103 0.053 1.934 0.053 0.115 0.115
## cuisine (h) 0.081 0.075 1.069 0.285 0.074 0.074
## variety (i) 0.134 0.053 2.512 0.012 0.197 0.197
## brand (j) -0.038 0.095 -0.400 0.689 -0.030 -0.030
## atmospher (k) 0.052 0.044 1.169 0.243 0.074 0.074
## decoratin (l) -0.109 0.048 -2.285 0.022 -0.152 -0.152
## commitment ~
## prfssnlsm (m) 0.160 0.129 1.240 0.215 0.129 0.129
## mode (n) -0.018 0.068 -0.260 0.795 -0.019 -0.019
## france (o) 0.223 0.067 3.327 0.001 0.192 0.192
## cuisine (p) 0.028 0.090 0.308 0.758 0.020 0.020
## variety (q) 0.101 0.055 1.840 0.066 0.114 0.114
## brand (r) -0.187 0.116 -1.614 0.106 -0.115 -0.115
## atmospher (s) 0.373 0.059 6.359 0.000 0.411 0.411
## decoratin (t) -0.024 0.058 -0.413 0.680 -0.026 -0.026
## cocreation ~
## prfssnlsm (u) -0.176 0.194 -0.908 0.364 -0.098 -0.098
## mode (v) 0.022 0.091 0.245 0.807 0.016 0.016
## france (w) -0.127 0.110 -1.152 0.249 -0.075 -0.075
## cuisine (x) -0.080 0.142 -0.560 0.575 -0.039 -0.039
## variety (y) -0.006 0.083 -0.074 0.941 -0.005 -0.005
## brand (z) 0.197 0.149 1.318 0.187 0.083 0.083
## atmospher (aa) 0.152 0.093 1.633 0.103 0.116 0.116
## decoratin (bb) -0.031 0.100 -0.311 0.756 -0.023 -0.023
## repurchase ~
## prfssnlsm (cc) -0.037 0.056 -0.655 0.513 -0.056 -0.056
## mode (dd) -0.011 0.028 -0.385 0.701 -0.022 -0.022
## france (ee) -0.034 0.031 -1.073 0.283 -0.056 -0.056
## cuisine (ff) 0.038 0.047 0.806 0.420 0.051 0.051
## variety (gg) -0.017 0.024 -0.688 0.491 -0.037 -0.037
## brand (hh) 0.077 0.052 1.490 0.136 0.091 0.091
## atmospher (ii) 0.040 0.029 1.375 0.169 0.085 0.085
## decoratin (jj) 0.010 0.027 0.358 0.720 0.020 0.020
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## decoration ~~
## atmosphere 0.728 0.086 8.422 0.000 0.467 0.467
## brand 0.407 0.054 7.531 0.000 0.470 0.470
## variety 0.708 0.076 9.364 0.000 0.442 0.442
## cuisine 0.417 0.053 7.922 0.000 0.417 0.417
## france 0.413 0.074 5.553 0.000 0.339 0.339
## mode 0.769 0.080 9.568 0.000 0.516 0.516
## professionalsm 0.744 0.078 9.528 0.000 0.655 0.655
## atmosphere ~~
## brand 0.370 0.064 5.772 0.000 0.418 0.418
## variety 0.732 0.084 8.665 0.000 0.447 0.447
## cuisine 0.301 0.053 5.668 0.000 0.295 0.295
## france 0.415 0.074 5.579 0.000 0.333 0.333
## mode 0.785 0.083 9.464 0.000 0.516 0.516
## professionalsm 0.552 0.073 7.616 0.000 0.476 0.476
## brand ~~
## variety 0.433 0.060 7.267 0.000 0.477 0.477
## cuisine 0.256 0.040 6.399 0.000 0.452 0.452
## france 0.211 0.039 5.423 0.000 0.305 0.305
## mode 0.477 0.064 7.438 0.000 0.565 0.565
## professionalsm 0.342 0.044 7.744 0.000 0.531 0.531
## variety ~~
## cuisine 0.327 0.050 6.583 0.000 0.312 0.312
## france 0.292 0.063 4.632 0.000 0.228 0.228
## mode 0.814 0.088 9.249 0.000 0.521 0.521
## professionalsm 0.717 0.075 9.576 0.000 0.602 0.602
## cuisine ~~
## france 0.469 0.050 9.313 0.000 0.587 0.587
## mode 0.317 0.042 7.576 0.000 0.325 0.325
## professionalsm 0.371 0.047 7.848 0.000 0.499 0.499
## france ~~
## mode 0.389 0.068 5.721 0.000 0.327 0.327
## professionalsm 0.336 0.051 6.602 0.000 0.370 0.370
## mode ~~
## professionalsm 0.667 0.068 9.845 0.000 0.602 0.602
## .cocreation ~~
## .repurchase -0.015 0.034 -0.434 0.664 -0.020 -0.020
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.622 0.000 4.995 3.786
## .Im4 4.999 0.057 87.009 0.000 4.999 3.712
## .Im5 5.036 0.057 87.765 0.000 5.036 3.787
## .Im20 4.672 0.064 73.268 0.000 4.672 3.125
## .Im21 5.139 0.058 88.093 0.000 5.139 3.750
## .Im22 4.280 0.065 65.575 0.000 4.280 2.802
## .Im11 5.653 0.049 115.355 0.000 5.653 4.944
## .Im12 5.665 0.049 116.260 0.000 5.665 4.986
## .Im13 5.448 0.052 105.700 0.000 5.448 4.527
## .Im1 4.792 0.057 84.272 0.000 4.792 3.600
## .Im2 4.858 0.055 88.351 0.000 4.858 3.781
## .Im10 6.100 0.037 162.837 0.000 6.100 6.936
## .Im14 6.138 0.037 165.572 0.000 6.138 7.093
## .Im6 5.828 0.051 114.014 0.000 5.828 4.858
## .Im7 5.754 0.052 110.958 0.000 5.754 4.756
## .Im17 5.025 0.053 94.433 0.000 5.025 4.042
## .Im18 4.595 0.060 76.160 0.000 4.595 3.287
## .Im16 5.135 0.052 99.250 0.000 5.135 4.270
## .Im19 5.145 0.048 106.953 0.000 5.145 4.576
## .SAT_1 5.343 0.044 122.780 0.000 5.343 5.239
## .SAT_2 5.482 0.043 127.736 0.000 5.482 5.455
## .SAT_3 5.458 0.050 109.045 0.000 5.458 4.774
## .COM_A1 4.287 0.062 69.635 0.000 4.287 2.983
## .COM_A2 3.887 0.069 56.723 0.000 3.887 2.420
## .COM_A3 3.543 0.070 50.824 0.000 3.543 2.178
## .COM_A4 3.456 0.074 46.674 0.000 3.456 1.991
## .C_CR1 2.679 0.083 32.267 0.000 2.679 1.375
## .C_CR3 3.261 0.088 37.085 0.000 3.261 1.572
## .C_CR4 2.786 0.084 33.126 0.000 2.786 1.405
## .C_REP1 4.283 0.031 136.245 0.000 4.283 5.859
## .C_REP2 4.507 0.027 167.452 0.000 4.507 7.250
## .C_REP3 4.677 0.024 193.058 0.000 4.677 8.445
## decoration 0.000 0.000 0.000
## atmosphere 0.000 0.000 0.000
## brand 0.000 0.000 0.000
## variety 0.000 0.000 0.000
## cuisine 0.000 0.000 0.000
## france 0.000 0.000 0.000
## mode 0.000 0.000 0.000
## professionalsm 0.000 0.000 0.000
## .satisfaction 0.000 0.000 0.000
## .commitment 0.000 0.000 0.000
## .cocreation 0.000 0.000 0.000
## .repurchase 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.214 0.042 5.082 0.000 0.214 0.123
## .Im4 0.108 0.031 3.507 0.000 0.108 0.060
## .Im5 0.747 0.066 11.357 0.000 0.747 0.422
## .Im20 0.644 0.076 8.530 0.000 0.644 0.288
## .Im21 0.708 0.093 7.634 0.000 0.708 0.377
## .Im22 0.557 0.076 7.288 0.000 0.557 0.239
## .Im11 0.817 0.091 8.950 0.000 0.817 0.625
## .Im12 0.309 0.055 5.592 0.000 0.309 0.240
## .Im13 0.389 0.055 7.021 0.000 0.389 0.269
## .Im1 0.090 0.052 1.716 0.086 0.090 0.051
## .Im2 0.302 0.051 5.914 0.000 0.302 0.183
## .Im10 0.118 0.029 4.073 0.000 0.118 0.153
## .Im14 0.066 0.022 3.010 0.003 0.066 0.088
## .Im6 0.466 0.067 6.998 0.000 0.466 0.324
## .Im7 0.158 0.072 2.198 0.028 0.158 0.108
## .Im17 0.092 0.046 1.990 0.047 0.092 0.060
## .Im18 0.524 0.088 5.965 0.000 0.524 0.268
## .Im16 0.602 0.071 8.415 0.000 0.602 0.416
## .Im19 0.345 0.052 6.650 0.000 0.345 0.273
## .SAT_1 0.262 0.038 6.976 0.000 0.262 0.252
## .SAT_2 0.332 0.061 5.485 0.000 0.332 0.329
## .SAT_3 0.798 0.165 4.832 0.000 0.798 0.610
## .COM_A1 0.757 0.074 10.270 0.000 0.757 0.366
## .COM_A2 0.779 0.084 9.326 0.000 0.779 0.302
## .COM_A3 0.880 0.079 11.170 0.000 0.880 0.333
## .COM_A4 0.875 0.080 10.987 0.000 0.875 0.290
## .C_CR1 1.047 0.144 7.285 0.000 1.047 0.276
## .C_CR3 1.369 0.192 7.125 0.000 1.369 0.318
## .C_CR4 1.378 0.204 6.766 0.000 1.378 0.351
## .C_REP1 0.179 0.027 6.733 0.000 0.179 0.334
## .C_REP2 0.051 0.012 4.160 0.000 0.051 0.133
## .C_REP3 0.131 0.012 10.620 0.000 0.131 0.428
## decoration 1.526 0.105 14.501 0.000 1.000 1.000
## atmosphere 1.591 0.138 11.533 0.000 1.000 1.000
## brand 0.491 0.088 5.558 0.000 1.000 1.000
## variety 1.682 0.114 14.718 0.000 1.000 1.000
## cuisine 0.655 0.066 9.882 0.000 1.000 1.000
## france 0.974 0.111 8.760 0.000 1.000 1.000
## mode 1.453 0.116 12.551 0.000 1.000 1.000
## professionalsm 0.845 0.101 8.367 0.000 1.000 1.000
## .satisfaction 0.449 0.063 7.166 0.000 0.576 0.576
## .commitment 0.862 0.088 9.757 0.000 0.659 0.659
## .cocreation 2.280 0.220 10.373 0.000 0.829 0.829
## .repurchase 0.237 0.025 9.638 0.000 0.667 0.667
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ae -0.164 0.078 -2.098 0.036 -0.091 -0.091
## af -0.003 0.022 -0.131 0.896 -0.002 -0.002
## ag -0.037 0.024 -1.532 0.126 -0.022 -0.022
## ah -0.029 0.031 -0.943 0.346 -0.014 -0.014
## ai -0.048 0.023 -2.066 0.039 -0.038 -0.038
## aj 0.014 0.034 0.406 0.685 0.006 0.006
## ak -0.019 0.018 -1.009 0.313 -0.014 -0.014
## al 0.039 0.025 1.564 0.118 0.029 0.029
## bm 0.087 0.073 1.204 0.229 0.048 0.048
## bn -0.010 0.037 -0.260 0.795 -0.007 -0.007
## bo 0.122 0.041 2.964 0.003 0.072 0.072
## bp 0.015 0.049 0.307 0.759 0.007 0.007
## bq 0.055 0.031 1.787 0.074 0.043 0.043
## br -0.102 0.066 -1.561 0.118 -0.043 -0.043
## bs 0.204 0.046 4.425 0.000 0.155 0.155
## bt -0.013 0.032 -0.410 0.682 -0.010 -0.010
## ce 0.099 0.033 2.945 0.003 0.152 0.152
## cf 0.002 0.013 0.130 0.896 0.003 0.003
## cg 0.022 0.012 1.860 0.063 0.037 0.037
## ch 0.017 0.017 1.003 0.316 0.023 0.023
## ci 0.029 0.013 2.212 0.027 0.063 0.063
## cj -0.008 0.021 -0.394 0.694 -0.010 -0.010
## ck 0.011 0.010 1.134 0.257 0.024 0.024
## cl -0.023 0.012 -1.972 0.049 -0.048 -0.048
## dm 0.030 0.024 1.217 0.223 0.045 0.045
## dn -0.003 0.012 -0.260 0.795 -0.007 -0.007
## do 0.041 0.014 2.932 0.003 0.068 0.068
## dp 0.005 0.017 0.308 0.758 0.007 0.007
## dq 0.019 0.010 1.777 0.076 0.040 0.040
## dr -0.035 0.022 -1.564 0.118 -0.041 -0.041
## ds 0.069 0.015 4.475 0.000 0.145 0.145
## dt -0.004 0.011 -0.413 0.679 -0.009 -0.009
## TE1C -0.253 0.181 -1.395 0.163 -0.140 -0.140
## TE2C 0.010 0.096 0.101 0.920 0.007 0.007
## TE3C -0.042 0.111 -0.377 0.706 -0.025 -0.025
## TE4C -0.093 0.152 -0.613 0.540 -0.045 -0.045
## TE5C 0.001 0.089 0.011 0.992 0.001 0.001
## TE6C 0.108 0.163 0.662 0.508 0.046 0.046
## TE7C 0.337 0.088 3.845 0.000 0.256 0.256
## TE8C -0.006 0.096 -0.057 0.954 -0.004 -0.004
## TE1R 0.091 0.059 1.556 0.120 0.141 0.141
## TE2R -0.012 0.038 -0.326 0.745 -0.025 -0.025
## TE3R 0.029 0.035 0.841 0.400 0.049 0.049
## TE4R 0.060 0.058 1.042 0.297 0.082 0.082
## TE5R 0.031 0.030 1.031 0.303 0.067 0.067
## TE6R 0.034 0.065 0.524 0.600 0.040 0.040
## TE7R 0.120 0.032 3.700 0.000 0.254 0.254
## TE8R -0.018 0.029 -0.614 0.539 -0.037 -0.037
## TIE1C -0.077 0.086 -0.887 0.375 -0.043 -0.043
## TIE2C -0.012 0.031 -0.401 0.689 -0.009 -0.009
## TIE3C 0.085 0.039 2.151 0.032 0.051 0.051
## TIE4C -0.014 0.047 -0.291 0.771 -0.007 -0.007
## TIE5C 0.007 0.032 0.220 0.826 0.006 0.006
## TIE6C -0.089 0.057 -1.568 0.117 -0.037 -0.037
## TIE7C 0.185 0.043 4.282 0.000 0.141 0.141
## TIE8C 0.026 0.035 0.725 0.468 0.019 0.019
## TIE1R 0.128 0.049 2.625 0.009 0.197 0.197
## TIE2R -0.002 0.022 -0.068 0.946 -0.003 -0.003
## TIE3R 0.063 0.021 3.016 0.003 0.104 0.104
## TIE4R 0.022 0.028 0.790 0.429 0.030 0.030
## TIE5R 0.047 0.019 2.448 0.014 0.103 0.103
## TIE6R -0.043 0.037 -1.159 0.246 -0.050 -0.050
## TIE7R 0.080 0.020 3.940 0.000 0.169 0.169
## TIE8R -0.028 0.018 -1.515 0.130 -0.057 -0.057- Latent Variables standardized loading : indicates the variance in the item explained through the contracts all are above 0.6 .
Global fit :
Sum_fit = summary(fit1, fit.measures=TRUE,standardized=TRUE)
Sum_fit$fit[c("chisq","df","rmsea","cfi")]## chisq df rmsea cfi
## 700.45462839 399.00000000 0.03696255 0.97374673Before examining the individual parameters, it is important to first assess the overall goodness of fit for the model. There are several criteria we can use to evaluate the global fit:
Chi-squared test: A low Chi-squared value, considering the degrees of freedom, indicates a good fit. The ratio of the Chi-squared value to the degrees of freedom should be below 5 for samples up to 1000. In this case, with 553 observations, we calculate the scaled measure as 632.247 / 399 = 1.584579 and the standard measure as 700.455 / 399 = 1.755526. Both ratios are below 5, indicating a good fit according to the Chi-squared test.
Root Mean Square Error of Approximation (RMSEA): A RMSEA value below 0.05 indicates a good model fit. In this case, we have an RMSEA of 0.037 and a Robust RMSEA of 0.034, which are both below the 0.05 threshold, suggesting that the model has a good fit based on RMSEA.
Comparative Fit Index (CFI): A CFI value above 0.95 indicates a good model fit. In this case, we have a CFI of 0.974, which is above the threshold, indicating a good fit based on CFI.
Given that the global fit measures meet the criteria for goodness of fit, we can conclude that the model is well-fitted. With a well-fitted model, we can proceed to analyze the individual parameter estimates with confidence.
modificationindices(fit1) %>%filter(mi>10)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 atmosphere =~ Im12 11.167 -0.115 -0.145 -0.128 -0.128
## 2 atmosphere =~ C_REP1 21.773 0.091 0.115 0.157 0.157
## 3 brand =~ C_CR4 11.166 0.305 0.214 0.108 0.108
## 4 variety =~ Im20 14.302 -0.150 -0.194 -0.130 -0.130
## 5 variety =~ Im12 10.903 -0.113 -0.147 -0.129 -0.129
## 6 variety =~ Im13 13.663 0.133 0.172 0.143 0.143
## 7 variety =~ C_REP1 10.720 0.056 0.073 0.100 0.100
## 8 cuisine =~ Im11 12.873 0.216 0.175 0.153 0.153
## 9 mode =~ Im12 17.448 -0.179 -0.215 -0.190 -0.190
## 10 mode =~ Im13 23.644 0.217 0.262 0.218 0.218
## 11 satisfaction =~ COM_A3 12.402 0.212 0.187 0.115 0.115
## 12 commitment =~ Im11 13.312 0.142 0.163 0.142 0.142
## 13 commitment =~ C_REP1 56.860 0.174 0.199 0.272 0.272
## 14 commitment =~ C_REP2 15.936 -0.079 -0.091 -0.146 -0.146
## 15 commitment =~ C_REP3 12.246 -0.065 -0.075 -0.135 -0.135
## 16 repurchase =~ SAT_2 15.148 0.256 0.153 0.152 0.152
## 17 repurchase =~ COM_A1 11.069 0.291 0.174 0.121 0.121
## 18 Im21 ~~ Im22 14.074 -0.239 -0.239 -0.381 -0.381
## 19 Im21 ~~ C_REP3 11.210 0.052 0.052 0.172 0.172
## 20 Im11 ~~ Im12 13.834 0.146 0.146 0.291 0.291
## 21 Im11 ~~ Im13 19.981 -0.183 -0.183 -0.324 -0.324
## 22 Im13 ~~ Im1 10.522 0.067 0.067 0.356 0.356
## 23 Im1 ~~ Im2 37.374 14.223 14.223 86.297 86.297
## 24 Im10 ~~ Im14 37.228 97.849 97.849 1110.833 1110.833
## 25 Im6 ~~ Im7 37.383 10.888 10.888 40.086 40.086
## 26 Im16 ~~ Im19 37.373 3.054 3.054 6.702 6.702
## 27 COM_A1 ~~ COM_A2 24.605 0.250 0.250 0.326 0.326
## 28 COM_A3 ~~ C_REP1 13.001 0.077 0.077 0.194 0.194
## 29 C_REP1 ~~ C_REP3 18.366 -0.056 -0.056 -0.368 -0.368
## 30 C_REP2 ~~ C_REP3 53.856 0.103 0.103 1.250 1.250
## 31 satisfaction ~~ commitment 37.384 0.215 0.346 0.346 0.346
## 32 satisfaction ~ cocreation 37.385 0.457 0.859 0.859 0.859
## 33 satisfaction ~ repurchase 37.384 1.354 0.915 0.915 0.915
## 34 satisfaction ~ commitment 37.384 0.250 0.324 0.324 0.324
## 35 commitment ~ cocreation 37.383 -1.343 -1.946 -1.946 -1.946
## 36 commitment ~ repurchase 37.384 2.236 1.166 1.166 1.166
## 37 commitment ~ satisfaction 37.384 0.480 0.370 0.370 0.370Local Fit Measures
#Local Fit
std.loadings <- inspect(fit1, what="std")$lambda
check = std.loadings
check[check > 0] <- 1
std.loadings[std.loadings == 0] <- NA
std.loadings2 <- std.loadings^2
std.theta <- inspect(fit1, what="std")$theta
#Individual item Reliability
IIR=std.loadings2/(colSums(std.theta) + std.loadings2)
IIR## decrtn atmsph brand varity cuisin france mode prfssn stsfct cmmtmn
## Im3 0.877 NA NA NA NA NA NA NA NA NA
## Im4 0.940 NA NA NA NA NA NA NA NA NA
## Im5 0.578 NA NA NA NA NA NA NA NA NA
## Im20 NA 0.712 NA NA NA NA NA NA NA NA
## Im21 NA 0.623 NA NA NA NA NA NA NA NA
## Im22 NA 0.761 NA NA NA NA NA NA NA NA
## Im11 NA NA 0.375 NA NA NA NA NA NA NA
## Im12 NA NA 0.760 NA NA NA NA NA NA NA
## Im13 NA NA 0.731 NA NA NA NA NA NA NA
## Im1 NA NA NA 0.949 NA NA NA NA NA NA
## Im2 NA NA NA 0.817 NA NA NA NA NA NA
## Im10 NA NA NA NA 0.847 NA NA NA NA NA
## Im14 NA NA NA NA 0.912 NA NA NA NA NA
## Im6 NA NA NA NA NA 0.676 NA NA NA NA
## Im7 NA NA NA NA NA 0.892 NA NA NA NA
## Im17 NA NA NA NA NA NA 0.940 NA NA NA
## Im18 NA NA NA NA NA NA 0.732 NA NA NA
## Im16 NA NA NA NA NA NA NA 0.584 NA NA
## Im19 NA NA NA NA NA NA NA 0.727 NA NA
## SAT_1 NA NA NA NA NA NA NA NA 0.748 NA
## SAT_2 NA NA NA NA NA NA NA NA 0.671 NA
## SAT_3 NA NA NA NA NA NA NA NA 0.390 NA
## COM_A1 NA NA NA NA NA NA NA NA NA 0.634
## COM_A2 NA NA NA NA NA NA NA NA NA 0.698
## COM_A3 NA NA NA NA NA NA NA NA NA 0.667
## COM_A4 NA NA NA NA NA NA NA NA NA 0.710
## C_CR1 NA NA NA NA NA NA NA NA NA NA
## C_CR3 NA NA NA NA NA NA NA NA NA NA
## C_CR4 NA NA NA NA NA NA NA NA NA NA
## C_REP1 NA NA NA NA NA NA NA NA NA NA
## C_REP2 NA NA NA NA NA NA NA NA NA NA
## C_REP3 NA NA NA NA NA NA NA NA NA NA
## cocrtn rprchs
## Im3 NA NA
## Im4 NA NA
## Im5 NA NA
## Im20 NA NA
## Im21 NA NA
## Im22 NA NA
## Im11 NA NA
## Im12 NA NA
## Im13 NA NA
## Im1 NA NA
## Im2 NA NA
## Im10 NA NA
## Im14 NA NA
## Im6 NA NA
## Im7 NA NA
## Im17 NA NA
## Im18 NA NA
## Im16 NA NA
## Im19 NA NA
## SAT_1 NA NA
## SAT_2 NA NA
## SAT_3 NA NA
## COM_A1 NA NA
## COM_A2 NA NA
## COM_A3 NA NA
## COM_A4 NA NA
## C_CR1 0.724 NA
## C_CR3 0.682 NA
## C_CR4 0.649 NA
## C_REP1 NA 0.666
## C_REP2 NA 0.867
## C_REP3 NA 0.572- All of them greater than 0.4 except for SAT_3 -SATISFACTION - How satisfied are you with Galeries Lafayette Berlin? suggest that the item is a weak indicator.
#Composite/Construct Reliability
sum.std.loadings<-colSums(std.loadings, na.rm=TRUE)^2
sum.std.theta<-rowSums(std.theta)
sum.std.theta=check*sum.std.theta
CR=sum.std.loadings/(sum.std.loadings+colSums(sum.std.theta))
CR## decoration atmosphere brand variety cuisine
## 0.9215577 0.8740995 0.8285131 0.9379212 0.9360530
## france mode professionalism satisfaction commitment
## 0.8785003 0.9103502 0.7914392 0.8173149 0.8934602
## cocreation repurchase
## 0.8670791 0.8749194- Should be above 0.6 ,indicating that the items are reliable and consistently measuring the underlying construct.
#Average Variance Extracted
std.loadings<- inspect(fit1, what="std")$lambda
std.loadings <- std.loadings^2
AVE=colSums(std.loadings)/(colSums(sum.std.theta)+colSums(std.loadings))
AVE## decoration atmosphere brand variety cuisine
## 0.7983096 0.6986333 0.6223003 0.8832435 0.8798287
## france mode professionalism satisfaction commitment
## 0.7841304 0.8359891 0.6555353 0.6029677 0.6771638
## cocreation repurchase
## 0.6850897 0.7014341- Should be higher than 0.5 , it is a measure of the amount of variance captured by a latent variable relative to the total variance due to measurement error
# Discriminant Validity
std_fit1=inspect(fit1, "std")
std_fit1$psi^2## decrtn atmsph brand varity cuisin france mode prfssn stsfct
## decoration 1.000
## atmosphere 0.218 1.000
## brand 0.221 0.175 1.000
## variety 0.195 0.200 0.228 1.000
## cuisine 0.174 0.087 0.204 0.097 1.000
## france 0.115 0.111 0.093 0.052 0.345 1.000
## mode 0.266 0.266 0.319 0.271 0.106 0.107 1.000
## professionalism 0.429 0.227 0.282 0.362 0.249 0.137 0.362 1.000
## satisfaction 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.332
## commitment 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## cocreation 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## repurchase 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## cmmtmn cocrtn rprchs
## decoration
## atmosphere
## brand
## variety
## cuisine
## france
## mode
## professionalism
## satisfaction
## commitment 0.435
## cocreation 0.000 0.688
## repurchase 0.000 0.000 0.445- It is important to compare these values to the AVE values to assess the discriminant validity of the measurement model. Discriminant validity is established when the AVE value for each latent variable is greater than the squared correlation between that latent variable and any other latent variable in the model. For example: For decoration and atmosphere, the squared correlation is 0.218 < AVE decoration and atmosphere are 0.798 and 0.699, respectively, discriminant validity is established between these two latent variables.
Plot the results:
semPaths(fit1, nCharNodes = 0, style = "lisrel", rotation = 2)
Are the mechanism driving satisfaction and affective commitment similar?
Indeed, the mechanisms driving satisfaction and affective commitment are not similar. Here’s a summary of the differences:
Mechanisms driving satisfaction:
Professionalism (e): Positive coefficient indicates that it has a positive impact on satisfaction.
Variety (i): Positive coefficient indicates that it has a positive impact on satisfaction.
Decoration (l): Negative coefficient indicates that it has a negative impact on satisfaction.
Mechanisms driving affective commitment:
France (o): Positive coefficient indicates that it has a positive impact on affective commitment.
Atmosphere (s): Positive coefficient indicates that it has a positive impact on affective commitment.
As we can see, the factors affecting satisfaction and affective commitment are different, and their respective impacts on these outcomes also vary. This highlights the distinct mechanisms driving satisfaction and affective commitment in Galeries Lafayetteperceived.
On the other hand, we can observe that satisfaction has a negative
coefficient on co-creation, which implies that the more satisfied
clients are, the less likely they are to participate in campaigns to
improve Galeries Lafayette. In contrast, affective commitment has a
positive relationship with co-creation, meaning that customers with
higher affective commitment are more likely to participate in such
campaigns.
Additionally, both affective commitment and satisfaction have a positive effect on repurchase intention from Galeries Lafayette. This indicates that clients who are more satisfied and have a stronger emotional attachment to the brand are more likely to return for future purchases.
Are satisfaction and affective commitment mediating the impact of image perceptions on outcomes? If yes for which outcomes?
In the regression analysis, we find that none of the eight factors have a direct effect on co-creation or repurchase intentions, as none of them show significant p-values:
Co-creation ~ all eight factors
Repurchase ~ all eight factors
However, we do observe indirect effects where satisfaction and affective commitment mediate the impact of image perceptions on these outcomes. We can identify significant indirect effects by examining the defined parameters:
- For ‘a’ (satisfaction on co-creation ), we have:
ae: ‘a’ represents satisfaction (in the co-creation regression) and ‘e’ for professionalism, satisfaction mediates the impact of professionalism on co-creation
- Professionalism → Satisfaction ( mediator )→ Co-creation
ai: ‘a’ represents satisfaction and ‘i’ for variety, satisfaction mediates the impact of variety on co-creation
- Variety → Satisfaction ( mediator ) → Co-creation
This relationship is significant, meaning that higher professionalism leads to increased customer satisfaction, which in turn results in lower co-creation (since customer satisfaction has a negative impact on co-creation, -0.357). The same reasoning applies to variety.
- For ‘b’ (affective commitment on Co-creation ), we have:
bo : ‘b’ represents Commitment and ‘o’ represents France .
- France → Affective Commitmen( mediator ) → Co-creation
bs: ‘b’ represents Commitment and ‘s’ for atmosphere.
- Atmosphere → Affective Commitmen( mediator ) → Co-creation
This relationship is significant, meaning that higher presence of French culture leads to increased customer affective commitment, which in turn results in higher co-creation . The same reasoning applies to atmosphere.
- For ‘c’ (satisfaction on repurchase intention), we have:
- ce: Professionalism → Satisfaction ( mediator ) → Repurchase Intention
- ci: Variety → Satisfaction ( mediator ) → Repurchase Intention
- cl: Decoration→ Satisfaction ( mediator ) → Repurchase Intention
All three have significant indirect effects on repurchase intention through satisfaction, with professionalism and variety having positive estimates, while decoration has a negative estimate.
- For ‘d’ (commitment on repurchase intention), we have:
do: France → Affective Commitmen( mediator ) → Repurchase Intention
ds: Atmosphere→ Affective Commitmen( mediator ) → Repurchase Intention
Both have significant indirect effects on repurchase intention through commitment, resulting in positive impacts on repurchase intention.
Question 3
What is driving the two distinct outcomes? Which image dimensions have the largest total effect on each of them?
Two distinct outcomes, co-creation and repurchase intention, are driven by different factors. Both satisfaction and affective commitment influence repurchase intention and co-creation, although their magnitudes differ.
# Total effects ( := TE)
# for cocreation
TE7C:= aa + (a*k) + (b*s)
# for repurchase
TE7R:= ii + (c*k) + (d*s)
# total indirect effect (:= TIE)
# for cocreation
TIE3C:= (a*g) + (b*o)
TIE7C:= (a*k) + (b*s)
# for repurchase
TIE1R:= (c*e) + (d*m)
TIE3R:= (c*g) + (d*o)
TIE5R:= (c*i) + (d*q)
TIE7R:= (c*k) + (d*s)
To identify which image dimensions have the largest total effect on each outcome, we can examine the defined parameter section. The total effects of TE7R and TE7C are the only significant ones, representing the image of atmosphere. Atmosphere has the largest total effect on repurchase intention and co-creation which are the most significant values.
For significant indirect effects, we have the following:
TIE3C : Indirect effects of France on co-creation
TIE7C Image of atmosphere has indirect effect on co-creation (as expected, since its total effect is significant)
TIE1R: Professionalism’s indirect effect on repurchase intention
TIE3R : Indirect effects of France on repurchase intention
TIE5R : Indirect effects of variety on repurchase intention
TIE7R: atmosphere indirect effect on repurchase intention
In summary, atmosphere has the largest total effect on both commitment and repurchase intention. Additionally, significant indirect effects include France on co-creation and repurchase intention, variety on repurchase intention, and professionalism on repurchase intention.